{ "types" : { "Bookmark" : { "pluralLabel" : "Bookmarks" }, "Publication" : { "pluralLabel" : "Publications" }, "GoldStandardPublication" : { "pluralLabel" : "GoldStandardPublications" }, "GoldStandardBookmark" : { "pluralLabel" : "GoldStandardBookmarks" }, "Tag" : { "pluralLabel" : "Tags" }, "User" : { "pluralLabel" : "Users" }, "Group" : { "pluralLabel" : "Groups" }, "Sphere" : { "pluralLabel" : "Spheres" } }, "properties" : { "count" : { "valueType" : "number" }, "date" : { "valueType" : "date" }, "changeDate" : { "valueType" : "date" }, "url" : { "valueType" : "url" }, "id" : { "valueType" : "url" }, "tags" : { "valueType" : "item" }, "user" : { "valueType" : "item" } }, "items" : [ { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/200b1431e5f9dcdaa289e80dcdb65278b/elkepeter", "tags" : [ "equations","hyperbolic","iadm","nonlinear","wirth" ], "intraHash" : "00b1431e5f9dcdaa289e80dcdb65278b", "interHash" : "3a7ff48e6f6c1a9d1251a9fb5bb71153", "label" : "About the solvability behaviour for special classes of nonlinear hyperbolic equations.", "user" : "elkepeter", "description" : "", "date" : "2021-10-21 07:36:38", "changeDate" : "2021-10-21 05:36:38", "count" : 4, "pub-type": "article", "journal": "Nonlinear Anal.", "year": "2003", "url": "https://doi.org/10.1016/S0362-546X(02)00096-2", "author": [ "Jens Wirth" ], "authors": [ {"first" : "Jens", "last" : "Wirth"} ], "volume": "52","number": "2","pages": "421--431", "mrclass" : "35L70 (35A22 35L15)", "mrreviewer" : "Nickolai A. Larkin", "fjournal" : "Nonlinear Analysis. Theory, Methods & Applications. An\r\n International Multidisciplinary Journal", "mrnumber" : "1937630", "issn" : "0362-546X", "doi" : "10.1016/S0362-546X(02)00096-2", "bibtexKey": "MR1937630" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/200b1431e5f9dcdaa289e80dcdb65278b/mathematik", "tags" : [ "equations","iadm","hyperbolic","from:elkepeter","wirth","nonlinear" ], "intraHash" : "00b1431e5f9dcdaa289e80dcdb65278b", "interHash" : "3a7ff48e6f6c1a9d1251a9fb5bb71153", "label" : "About the solvability behaviour for special classes of nonlinear hyperbolic equations.", "user" : "mathematik", "description" : "", "date" : "2021-10-21 07:36:38", "changeDate" : "2021-10-21 05:36:38", "count" : 4, "pub-type": "article", "journal": "Nonlinear Anal.", "year": "2003", "url": "https://doi.org/10.1016/S0362-546X(02)00096-2", "author": [ "Jens Wirth" ], "authors": [ {"first" : "Jens", "last" : "Wirth"} ], "volume": "52","number": "2","pages": "421--431", "mrclass" : "35L70 (35A22 35L15)", "mrreviewer" : "Nickolai A. Larkin", "fjournal" : "Nonlinear Analysis. Theory, Methods & Applications. An\r\n International Multidisciplinary Journal", "mrnumber" : "1937630", "issn" : "0362-546X", "doi" : "10.1016/S0362-546X(02)00096-2", "bibtexKey": "MR1937630" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/273ba9993051913de4cc8e152a2559504/elkepeter", "tags" : [ "hyperbolic","iadm","systems","wirth" ], "intraHash" : "73ba9993051913de4cc8e152a2559504", "interHash" : "418dd3b8dc7be736cf3345390b10e4d0", "label" : "Dispersive estimates for T-dependent hyperbolic systems", "user" : "elkepeter", "description" : "", "date" : "2021-10-21 07:26:46", "changeDate" : "2021-10-21 05:26:46", "count" : 3, "pub-type": "article", "journal": "Rend. Semin. Mat. Univ. Politec. Torino", "year": "2008", "url": "", "author": [ "M. Ruzhansky","J. Wirth" ], "authors": [ {"first" : "M.", "last" : "Ruzhansky"}, {"first" : "J.", "last" : "Wirth"} ], "volume": "66","number": "4","pages": "339--349", "mrclass" : "35L45", "mrreviewer" : "Alessandro Morando", "fjournal" : "Rendiconti del Seminario Matematico. Università e Politecnico\r\n Torino", "mrnumber" : "2537624", "issn" : "0373-1243", "bibtexKey": "MR2537624" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2327bb09e085baf10c8d35ed75aa04254/elkepeter", "tags" : [ "hyperbolic","iadm","phenomena","systems","wirth" ], "intraHash" : "327bb09e085baf10c8d35ed75aa04254", "interHash" : "e60ff2d4a02213156e4b722f20debd6f", "label" : "Diffusion phenomena for partially dissipative hyperbolic\r\n systems", "user" : "elkepeter", "description" : "", "date" : "2021-10-21 07:12:33", "changeDate" : "2021-10-21 05:12:33", "count" : 3, "pub-type": "article", "journal": "J. Math. Anal. Appl.", "year": "2014", "url": "https://doi.org/10.1016/j.jmaa.2014.01.034", "author": [ "Jens Wirth" ], "authors": [ {"first" : "Jens", "last" : "Wirth"} ], "volume": "414","number": "2","pages": "666--677", "mrclass" : "35M31 (35B40 35B45)", "fjournal" : "Journal of Mathematical Analysis and Applications", "mrnumber" : "3167988", "issn" : "0022-247X", "doi" : "10.1016/j.jmaa.2014.01.034", "bibtexKey": "MR3167988" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2327bb09e085baf10c8d35ed75aa04254/mathematik", "tags" : [ "iadm","systems","hyperbolic","from:elkepeter","phenomena","wirth" ], "intraHash" : "327bb09e085baf10c8d35ed75aa04254", "interHash" : "e60ff2d4a02213156e4b722f20debd6f", "label" : "Diffusion phenomena for partially dissipative hyperbolic\r\n systems", "user" : "mathematik", "description" : "", "date" : "2021-10-21 07:12:33", "changeDate" : "2021-10-21 05:12:33", "count" : 3, "pub-type": "article", "journal": "J. Math. Anal. Appl.", "year": "2014", "url": "https://doi.org/10.1016/j.jmaa.2014.01.034", "author": [ "Jens Wirth" ], "authors": [ {"first" : "Jens", "last" : "Wirth"} ], "volume": "414","number": "2","pages": "666--677", "mrclass" : "35M31 (35B40 35B45)", "fjournal" : "Journal of Mathematical Analysis and Applications", "mrnumber" : "3167988", "issn" : "0022-247X", "doi" : "10.1016/j.jmaa.2014.01.034", "bibtexKey": "MR3167988" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2a40683a8ca5ef9739a9c29982cd65259/elkepeter", "tags" : [ "Lebesgue","hyperbolic","iadm","spaces","systems","wirth" ], "intraHash" : "a40683a8ca5ef9739a9c29982cd65259", "interHash" : "7f25941f6a1d02cc17fe27fb9e89104f", "label" : "Variable Lebesgue spaces and hyperbolic systems", "user" : "elkepeter", "description" : "", "date" : "2021-10-21 07:11:10", "changeDate" : "2021-10-21 05:11:10", "count" : 3, "pub-type": "book", "series": "Advanced Courses in Mathematics. CRM Barcelona","publisher":"Birkhäuser/Springer, Basel", "year": "2014", "url": "", "author": [ "David Cruz-Uribe","Alberto Fiorenza","Michael Ruzhansky","Jens Wirth" ], "authors": [ {"first" : "David", "last" : "Cruz-Uribe"}, {"first" : "Alberto", "last" : "Fiorenza"}, {"first" : "Michael", "last" : "Ruzhansky"}, {"first" : "Jens", "last" : "Wirth"} ], "pages": "x+169","note": "Selected lecture notes from the Advanced Courses on Approximation Theory and Fourier Analysis held at the Centre de Recerca Matemàtica, Barcelona, November 7--11, 2011, Edited by Sergey Tikhonov", "mrclass" : "35-06 (42-06)", "isbn" : "978-3-0348-0839-2; 978-3-0348-0840-8", "mrnumber" : "3364250", "bibtexKey": "MR3364250" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2a40683a8ca5ef9739a9c29982cd65259/mathematik", "tags" : [ "Lebesgue","iadm","systems","hyperbolic","from:elkepeter","spaces","wirth" ], "intraHash" : "a40683a8ca5ef9739a9c29982cd65259", "interHash" : "7f25941f6a1d02cc17fe27fb9e89104f", "label" : "Variable Lebesgue spaces and hyperbolic systems", "user" : "mathematik", "description" : "", "date" : "2021-10-21 07:11:10", "changeDate" : "2021-10-21 05:11:10", "count" : 3, "pub-type": "book", "series": "Advanced Courses in Mathematics. CRM Barcelona","publisher":"Birkhäuser/Springer, Basel", "year": "2014", "url": "", "author": [ "David Cruz-Uribe","Alberto Fiorenza","Michael Ruzhansky","Jens Wirth" ], "authors": [ {"first" : "David", "last" : "Cruz-Uribe"}, {"first" : "Alberto", "last" : "Fiorenza"}, {"first" : "Michael", "last" : "Ruzhansky"}, {"first" : "Jens", "last" : "Wirth"} ], "pages": "x+169","note": "Selected lecture notes from the Advanced Courses on Approximation Theory and Fourier Analysis held at the Centre de Recerca Matemàtica, Barcelona, November 7--11, 2011, Edited by Sergey Tikhonov", "mrclass" : "35-06 (42-06)", "isbn" : "978-3-0348-0839-2; 978-3-0348-0840-8", "mrnumber" : "3364250", "bibtexKey": "MR3364250" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/288238cd0c7128fc5060966569380dc94/elkepeter", "tags" : [ "Hyperbolic","iadm","wirth" ], "intraHash" : "88238cd0c7128fc5060966569380dc94", "interHash" : "a2d048399dda908eaa77d80352e89d77", "label" : "Asymptotic behaviour of solutions to hyperbolic equations and systems", "user" : "elkepeter", "description" : "", "date" : "2021-10-21 07:10:04", "changeDate" : "2021-10-21 05:10:04", "count" : 3, "pub-type": "incollection", "booktitle": "Variable Lebesgue spaces and hyperbolic systems","series": "Adv. Courses Math. CRM Barcelona","publisher":"Birkhäuser/Springer, Basel", "year": "2014", "url": "", "author": [ "Michael Ruzhansky","Jens Wirth" ], "authors": [ {"first" : "Michael", "last" : "Ruzhansky"}, {"first" : "Jens", "last" : "Wirth"} ], "pages": "91--169", "mrclass" : "35L45 (35B30 35B40 35L15 35L30 35S30)", "mrreviewer" : "Hidetoshi Tahara", "mrnumber" : "3364252", "bibtexKey": "MR3364252" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/288238cd0c7128fc5060966569380dc94/mathematik", "tags" : [ "iadm","from:elkepeter","Hyperbolic","wirth" ], "intraHash" : "88238cd0c7128fc5060966569380dc94", "interHash" : "a2d048399dda908eaa77d80352e89d77", "label" : "Asymptotic behaviour of solutions to hyperbolic equations and systems", "user" : "mathematik", "description" : "", "date" : "2021-10-21 07:10:04", "changeDate" : "2021-10-21 05:10:04", "count" : 3, "pub-type": "incollection", "booktitle": "Variable Lebesgue spaces and hyperbolic systems","series": "Adv. Courses Math. CRM Barcelona","publisher":"Birkhäuser/Springer, Basel", "year": "2014", "url": "", "author": [ "Michael Ruzhansky","Jens Wirth" ], "authors": [ {"first" : "Michael", "last" : "Ruzhansky"}, {"first" : "Jens", "last" : "Wirth"} ], "pages": "91--169", "mrclass" : "35L45 (35B30 35B40 35L15 35L30 35S30)", "mrreviewer" : "Hidetoshi Tahara", "mrnumber" : "3364252", "bibtexKey": "MR3364252" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/25e21dff3cecacd994cb8f6e0fa2fb9e2/elkepeter", "tags" : [ "Hyperbolic","IADM","Systems","Wirth" ], "intraHash" : "5e21dff3cecacd994cb8f6e0fa2fb9e2", "interHash" : "f5aac40afd1eefb0d1689ca23ec1e520", "label" : "Regular singular problems for hyperbolic systems and their\r\n asymptotic integration", "user" : "elkepeter", "description" : "", "date" : "2021-10-21 07:02:24", "changeDate" : "2021-10-21 05:02:24", "count" : 4, "pub-type": "incollection", "booktitle": "New trends in analysis and interdisciplinary applications","series": "Trends Math. Res. Perspect.","publisher":"Birkhäuser/Springer, Cham", "year": "2017", "url": "https://doi.org/10.1007/978-3-319-48812-7_70", "author": [ "Jens Wirth" ], "authors": [ {"first" : "Jens", "last" : "Wirth"} ], "pages": "553--561", "mrclass" : "35L52", "mrnumber" : "3695687", "doi" : "10.1007/978-3-319-48812-7_70", "bibtexKey": "MR3695687" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/25e21dff3cecacd994cb8f6e0fa2fb9e2/mathematik", "tags" : [ "IADM","from:elkepeter","Hyperbolic","Wirth","Systems" ], "intraHash" : "5e21dff3cecacd994cb8f6e0fa2fb9e2", "interHash" : "f5aac40afd1eefb0d1689ca23ec1e520", "label" : "Regular singular problems for hyperbolic systems and their\r\n asymptotic integration", "user" : "mathematik", "description" : "", "date" : "2021-10-21 07:02:24", "changeDate" : "2021-10-21 05:02:24", "count" : 4, "pub-type": "incollection", "booktitle": "New trends in analysis and interdisciplinary applications","series": "Trends Math. Res. Perspect.","publisher":"Birkhäuser/Springer, Cham", "year": "2017", "url": "https://doi.org/10.1007/978-3-319-48812-7_70", "author": [ "Jens Wirth" ], "authors": [ {"first" : "Jens", "last" : "Wirth"} ], "pages": "553--561", "mrclass" : "35L52", "mrnumber" : "3695687", "doi" : "10.1007/978-3-319-48812-7_70", "bibtexKey": "MR3695687" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2d43a1d49e6b5e1e3246e8cd38c7f9b83/fabianmeyer", "tags" : [ "hyperbolic","ians","uq" ], "intraHash" : "d43a1d49e6b5e1e3246e8cd38c7f9b83", "interHash" : "703e0fcbc3febb7a7193c9b86b404f4e", "label" : "A hyperbolicity-preserving discontinuous stochastic Galerkin scheme\r\n\tfor uncertain hyperbolic systems of equations", "user" : "fabianmeyer", "description" : "", "date" : "2018-10-23 10:06:30", "changeDate" : "2018-10-23 08:06:30", "count" : 3, "pub-type": "techreport", "year": "2018", "url": "https://arxiv.org/abs/1805.10177", "author": [ "F. Meyer","L. Schlachter","F. Schneider" ], "authors": [ {"first" : "F.", "last" : "Meyer"}, {"first" : "L.", "last" : "Schlachter"}, {"first" : "F.", "last" : "Schneider"} ], "abstract": "Intrusive Uncertainty Quantification methods such as stochastic Galerkin\r\n\tare gaining popularity, whereas the classical stochastic Galerkin\r\n\tapproach is not ensured to preserve hyperbolicity of the underlying\r\n\thyperbolic system. We present a modification of this method that\r\n\tuses a slope limiter to retain admissible solutions of the system,\r\n\twhile providing high-order approximations in the physical and stochastic\r\n\tspace. This is done using spatial discontinuous Galerkin and a Multi-Element\r\n\tstochastic Galerkin ansatz in the random space. We analyze the convergence\r\n\tof the resulting scheme and apply it to the compressible Euler equations\r\n\twith different uncertain initial states. The numerical results underline\r\n\tthe strength of our method if discontinuities are present in the\r\n\tuncertainty of the solution.", "owner" : "meyerfn", "__markedentry" : "[szur:6]", "bibtexKey": "meyer2018hyperbolicitypreserving" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/24b6636216b66dfdfd50ca53bb93685de/mathematik", "tags" : [ "(SUPG),","Galerkin,","Petrove-Galerkin","adaptive","conservation","continuous","discontinuous","from:mhartmann","hyperbolic","ians","laws,","method,","postprocessing","spectral","streamline","upwind","viscosity,","vorlaeufig","wavelet" ], "intraHash" : "4b6636216b66dfdfd50ca53bb93685de", "interHash" : "c8972e3ab25e760174ed7741330758be", "label" : "An adaptive wavelet space-time SUPG method for hyperbolic conservation\n\tlaws", "user" : "mathematik", "description" : "", "date" : "2018-07-20 10:54:20", "changeDate" : "2019-12-18 14:37:55", "count" : 2, "pub-type": "article", "journal": "Numerical Methods for Partial Differential Equations", "year": "2017", "url": "https://onlinelibrary.wiley.com/doi/abs/10.1002/num.22180", "author": [ "Hadi Minbashian","Hojatolah Adibi","Mehdi Dehghan" ], "authors": [ {"first" : "Hadi", "last" : "Minbashian"}, {"first" : "Hojatolah", "last" : "Adibi"}, {"first" : "Mehdi", "last" : "Dehghan"} ], "volume": "33","number": "6","pages": "2062-2089","abstract": "This article concerns with incorporating wavelet bases into existing\n\tstreamline upwind Petrov-Galerkin (SUPG) methods for the numerical\n\tsolution of nonlinear hyperbolic conservation laws which are known\n\tto develop shock solutions. Here, we utilize an SUPG formulation\n\tusing continuous Galerkin in space and discontinuous Galerkin in\n\ttime. The main motivation for such a combination is that these methods\n\thave good stability properties thanks to adding diffusion in the\n\tdirection of streamlines. But they are more expensive than explicit\n\tsemidiscrete methods as they have to use space-time formulations.\n\tUsing wavelet bases we maintain the stability properties of SUPG\n\tmethods while we reduce the cost of these methods significantly through\n\tnatural adaptivity of wavelet expansions. In addition, wavelet bases\n\thave a hierarchical structure. We use this property to numerically\n\tinvestigate the hierarchical addition of an artificial diffusion\n\tfor further stabilization in spirit of spectral diffusion. Furthermore,\n\twe add the hierarchical diffusion only in the vicinity of discontinuities\n\tusing the feature of wavelet bases in detection of location of discontinuities.\n\tAlso, we again use the last feature of the wavelet bases to perform\n\ta postprocessing using a denosing technique based on a minimization\n\tformulation to reduce Gibbs oscillations near discontinuities while\n\tkeeping other regions intact. Finally, we show the performance of\n\tthe proposed combination through some numerical examples including\n\tBurgers�, transport, and wave equations as well as systems of shallow\n\twater equations.� 2017 Wiley Periodicals, Inc. Numer Methods Partial\n\tDifferential Eq 33: 2062�2089, 2017", "owner" : "seusdd", "doi" : "10.1002/num.22180", "eprint" : "https://onlinelibrary.wiley.com/doi/pdf/10.1002/num.22180", "bibtexKey": "minbashian2017adaptive" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/24b6636216b66dfdfd50ca53bb93685de/mhartmann", "tags" : [ "(SUPG),","Galerkin,","Petrove-Galerkin","adaptive","conservation","continuous","discontinuous","hyperbolic","laws,","method,","postprocessing","spectral","streamline","upwind","viscosity,","vorlaeufig","wavelet" ], "intraHash" : "4b6636216b66dfdfd50ca53bb93685de", "interHash" : "c8972e3ab25e760174ed7741330758be", "label" : "An adaptive wavelet space-time SUPG method for hyperbolic conservation\n\tlaws", "user" : "mhartmann", "description" : "", "date" : "2018-07-20 10:54:15", "changeDate" : "2018-07-20 08:54:15", "count" : 2, "pub-type": "article", "journal": "Numerical Methods for Partial Differential Equations", "year": "2017", "url": "https://onlinelibrary.wiley.com/doi/abs/10.1002/num.22180", "author": [ "Hadi Minbashian","Hojatolah Adibi","Mehdi Dehghan" ], "authors": [ {"first" : "Hadi", "last" : "Minbashian"}, {"first" : "Hojatolah", "last" : "Adibi"}, {"first" : "Mehdi", "last" : "Dehghan"} ], "volume": "33","number": "6","pages": "2062-2089","abstract": "This article concerns with incorporating wavelet bases into existing\n\tstreamline upwind Petrov-Galerkin (SUPG) methods for the numerical\n\tsolution of nonlinear hyperbolic conservation laws which are known\n\tto develop shock solutions. Here, we utilize an SUPG formulation\n\tusing continuous Galerkin in space and discontinuous Galerkin in\n\ttime. The main motivation for such a combination is that these methods\n\thave good stability properties thanks to adding diffusion in the\n\tdirection of streamlines. But they are more expensive than explicit\n\tsemidiscrete methods as they have to use space-time formulations.\n\tUsing wavelet bases we maintain the stability properties of SUPG\n\tmethods while we reduce the cost of these methods significantly through\n\tnatural adaptivity of wavelet expansions. In addition, wavelet bases\n\thave a hierarchical structure. We use this property to numerically\n\tinvestigate the hierarchical addition of an artificial diffusion\n\tfor further stabilization in spirit of spectral diffusion. Furthermore,\n\twe add the hierarchical diffusion only in the vicinity of discontinuities\n\tusing the feature of wavelet bases in detection of location of discontinuities.\n\tAlso, we again use the last feature of the wavelet bases to perform\n\ta postprocessing using a denosing technique based on a minimization\n\tformulation to reduce Gibbs oscillations near discontinuities while\n\tkeeping other regions intact. Finally, we show the performance of\n\tthe proposed combination through some numerical examples including\n\tBurgers�, transport, and wave equations as well as systems of shallow\n\twater equations.� 2017 Wiley Periodicals, Inc. Numer Methods Partial\n\tDifferential Eq 33: 2062�2089, 2017", "owner" : "seusdd", "doi" : "10.1002/num.22180", "eprint" : "https://onlinelibrary.wiley.com/doi/pdf/10.1002/num.22180", "bibtexKey": "minbashian2017adaptive" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/24ab79299cbb2e8198984be253e0619cb/ulrikeoffenbeck", "tags" : [ "hyperbolic","materials","tetradymites" ], "intraHash" : "4ab79299cbb2e8198984be253e0619cb", "interHash" : "b2b853b880882ebcf80676c42e170c83", "label" : "Tetradymites as Natural Hyperbolic Materials for the Near-Infrared to Visible", "user" : "ulrikeoffenbeck", "description" : "", "date" : "2018-03-08 15:35:16", "changeDate" : "2018-03-08 14:35:16", "count" : 1, "pub-type": "article", "journal": "ACS Photonics","publisher":"American Chemical Society (ACS)", "year": "2014", "url": "https://doi.org/10.1021%2Fph500296e", "author": [ "Moritz Esslinger","Ralf Vogelgesang","Nahid Talebi","Worawut Khunsin","Pascal Gehring","Stefano de Zuani","Bruno Gompf","Klaus Kern" ], "authors": [ {"first" : "Moritz", "last" : "Esslinger"}, {"first" : "Ralf", "last" : "Vogelgesang"}, {"first" : "Nahid", "last" : "Talebi"}, {"first" : "Worawut", "last" : "Khunsin"}, {"first" : "Pascal", "last" : "Gehring"}, {"first" : "Stefano", "last" : "de Zuani"}, {"first" : "Bruno", "last" : "Gompf"}, {"first" : "Klaus", "last" : "Kern"} ], "volume": "1","number": "12","pages": "1285-1289", "doi" : "10.1021/ph500296e", "bibtexKey": "Esslinger_2014" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2ca15e451be40b14c5bec014bafe54360/hermann", "tags" : [ "Carlo","Gaussian","Monte","Ornstein-Uhlenbeck","differential","equation;","field;","field}","finite","flux","function;","hyperbolic","method;","partial","process;","quantification;","random","spatiotemporal","uncertainty","volume","{stochastic" ], "intraHash" : "ca15e451be40b14c5bec014bafe54360", "interHash" : "b1b958721ff8d51a5d30f7154c6f3414", "label" : "UNCERTAINTY QUANTIFICATION FOR HYPERBOLIC CONSERVATION LAWS WITH FLUX\n COEFFICIENTS GIVEN BY SPATIOTEMPORAL RANDOM FIELDS", "user" : "hermann", "description" : "", "date" : "2017-05-18 11:32:12", "changeDate" : "2017-05-18 09:32:12", "count" : 13, "pub-type": "article", "journal": "SIAM JOURNAL ON SCIENTIFIC COMPUTING","publisher":"SIAM PUBLICATIONS","address":"3600 UNIV CITY SCIENCE CENTER, PHILADELPHIA, PA 19104-2688 USA", "year": "{2016}", "url": "", "author": [ "Andrea Barth","Franz G. Fuchs" ], "authors": [ {"first" : "Andrea", "last" : "Barth"}, {"first" : "Franz G.", "last" : "Fuchs"} ], "volume": "38","number": "4","pages": "A2209-A2231","abstract": "In this paper hyperbolic partial differential equations (PDEs) with\n random coefficients are discussed. We consider the challenging problem\n of flux functions with coefficients modeled by spatiotemporal random\n fields. Those fields are given by correlated Gaussian random fields in\n space and Ornstein-Uhlenbeck processes in time. The resulting system of\n equations consists of a stochastic differential equation for each random\n parameter coupled to the hyperbolic conservation law. We de fine an\n appropriate solution concept in this setting and analyze errors and\n convergence of discretization methods. A novel discretization framework,\n based on Monte Carlo finite volume methods, is presented for the robust\n computation of moments of solutions to those random hyperbolic PDEs. We\n showcase the approach on two examples which appear in applications-the\n magnetic induction equation and linear acoustics both with a\n spatiotemporal random background velocity field.", "author-email" : "andrea.barth@mathematik.uni-stuttgart.de\n franzgeorgfuchs@gmail.com", "issn" : "1064-8275", "keywords-plus" : "FINITE-VOLUME METHODS; LINEAR TRANSPORT-EQUATION;\n DIFFERENTIAL-EQUATIONS; ADVECTION EQUATION; POLYNOMIAL CHAOS; SCHEMES;\n MULTIDIMENSIONS; SPEED", "funding-acknowledgement" : "German Research Foundation (DFG) as part of Cluster of Excellence in\n Simulation Technology at the University of Stuttgart [EXC 310/2]", "research-areas" : "Mathematics", "eissn" : "1095-7197", "number-of-cited-references" : "46", "affiliation" : "Barth, A (Reprint Author), Univ Stuttgart, SimTech, D-70569 Stuttgart, Germany.\n Barth, Andrea, Univ Stuttgart, SimTech, D-70569 Stuttgart, Germany.\n Fuchs, Franz G., SINTEF, N-0314 Oslo, Norway.", "web-of-science-categories" : "Mathematics, Applied", "language" : "English", "funding-text" : "SimTech, University of Stuttgart, 70569 Stuttgart, Germany\n (andrea.barth@mathematik.unistuttgart.de). This author's work was\n supported by the German Research Foundation (DFG) as part of the Cluster\n of Excellence in Simulation Technology (EXC 310/2) at the University of\n Stuttgart, and it is gratefully acknowledged.", "times-cited" : "0", "doi" : "10.1137/15M1027723", "bibtexKey": "ISI:000385283400013" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2d243188d800231a5e87752565bf2f54c/ik", "tags" : [ "HSG","Stochastic-Galerkin","UQ","clarifier-thickener","hyperbolic","myown" ], "intraHash" : "d243188d800231a5e87752565bf2f54c", "interHash" : "3e75df22fa8ec60ad20e3c0a1e9f2a72", "label" : "A hybrid stochastic Galerkin method for uncertainty quantification applied to a conservation law modelling a clarifier-thickener unit", "user" : "ik", "description" : "A hybrid stochastic Galerkin method for uncertainty quantification applied to a conservation law modelling a clarifier-thickener unit - Bürger - 2013 - ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik - Wiley Online Library", "date" : "2016-04-26 10:37:26", "changeDate" : "2016-04-26 12:08:02", "count" : 1, "pub-type": "article", "journal": "ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik","publisher":"WILEY-VCH Verlag", "year": "2014", "url": "http://dx.doi.org/10.1002/zamm.201200174", "author": [ "R. Bürger","I. Kröker","C. Rohde" ], "authors": [ {"first" : "R.", "last" : "Bürger"}, {"first" : "I.", "last" : "Kröker"}, {"first" : "C.", "last" : "Rohde"} ], "volume": "94","number": "10","pages": "793--817","abstract": "The continuous sedimentation process in a clarifier-thickener can be described by a scalar nonlinear conservation law for the local solids volume fraction. The flux density function is discontinuous with respect to spatial position due to feed and discharge mechanisms. Typically, the feed flow cannot be given deterministically and efficient numerical simulation requires a concept for quantifying uncertainty. In this paper uncertainty quantification is expressed by a new hybrid stochastic Galerkin (HSG) method that extends the classical polynomial chaos approximation by multiresolution discretization in the stochastic space. The new approach leads to a deterministic hyperbolic system for a finite number of stochastic moments which is however partially decoupled and thus allows efficient parallelisation. The complexity of the problem is further reduced by stochastic adaptivity. For the approximate solution of the resulting high-dimensional system a finite volume scheme is introduced. Numerical experiments cover one- and two-dimensional situations.", "issn" : "1521-4001", "doi" : "10.1002/zamm.201200174", "bibtexKey": "ZAMM:ZAMM201200174" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2fbdb6c6af9777516523af2681bbede3a/ik", "tags" : [ "hyperbolic","multiplicative-noise","myown" ], "intraHash" : "fbdb6c6af9777516523af2681bbede3a", "interHash" : "64860e369eaa4c497300fa7d8ca256c6", "label" : "Finite volume schemes for hyperbolic balance laws with multiplicative noise", "user" : "ik", "description" : "", "date" : "2016-04-26 10:34:30", "changeDate" : "2016-04-26 08:35:20", "count" : 6, "pub-type": "article", "journal": "Applied Numerical Mathematics", "year": "2012", "url": "http://www.sciencedirect.com/science/article/pii/S016892741100033X", "author": [ "I. Kröker","C. Rohde" ], "authors": [ {"first" : "I.", "last" : "Kröker"}, {"first" : "C.", "last" : "Rohde"} ], "volume": "62","number": "4","pages": "441 - 456","note": "Third Chilean Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE 2010)","abstract": "We consider finite volume schemes for a scalar stochastic balance law with multiplicative noise. For a class of monotone numerical fluxes we establish the pathwise convergence of a semi-discrete finite volume solution towards a stochastic entropy solution. Main tool is a stochastic version of the compensated compactness approach. The approach relies solely on L p -estimates. It avoids the use of a maximum principle and total-variation estimates. These are typical tools in the deterministic case but are not available for the non-deterministic model. Numerical results illustrate the analytical findings.", "issn" : "0168-9274", "doi" : "http://dx.doi.org/10.1016/j.apnum.2011.01.011", "bibtexKey": "Kröker2012441" } ] }