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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/24b6636216b66dfdfd50ca53bb93685de/mhartmann", "tags" : [ "Petrove-Galerkin","postprocessing","hyperbolic","Galerkin,","laws,","spectral","streamline","upwind","(SUPG),","viscosity,","adaptive","conservation","continuous","wavelet","discontinuous","vorlaeufig","method," ], "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/2ca15e451be40b14c5bec014bafe54360/hermann", "tags" : [ "hyperbolic","field;","field}","finite","Carlo","quantification;","Monte","method;","differential","uncertainty","random","Ornstein-Uhlenbeck","{stochastic","volume","flux","equation;","spatiotemporal","Gaussian","partial","process;","function;" ], "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" } ] }