{ "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/2769be1510640e0e78e217c26c4dffbb5/mhartmann", "tags" : [ "Nonlinear","domain,","Brinkman","boundary","problem,","Layer","76M","Lipschitz","42B20,","Stokes","46E35,","35J25,","and","value","vorlaeufig","potential","operators,","76D," ], "intraHash" : "769be1510640e0e78e217c26c4dffbb5", "interHash" : "d6d8c49bb72357b5a9ac7fe494eb266e", "label" : "Nonlinear Neumann-Transmission Problems for Stokes and Brinkman Equations\n\ton Euclidean Lipschitz Domains", "user" : "mhartmann", "description" : "", "date" : "2018-07-20 10:54:15", "changeDate" : "2018-07-20 08:54:15", "count" : 2, "pub-type": "article", "journal": "Potential Analysis", "year": "2013", "url": "http://dx.doi.org/10.1007/s11118-012-9310-0", "author": [ "Mirela Kohr","Massimo Lanza de Cristoforis","Wolfgang L. Wendland" ], "authors": [ {"first" : "Mirela", "last" : "Kohr"}, {"first" : "Massimo", "last" : "Lanza de Cristoforis"}, {"first" : "Wolfgang L.", "last" : "Wendland"} ], "volume": "38","pages": "1123-1171", "issn" : "0926-2601", "language" : "English", "doi" : "10.1007/s.11118-012-9310-0", "bibtexKey": "kohr2013nonlinear" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/29db316fbe639db8fe7dbd32263b10ad6/mhartmann", "tags" : [ "boundary","Sobolev--Slobodetskii","refinement,","spaces,","Galerkin","problems,","spaces","graded","Sobolev","discontinuous","value","weighted","vorlaeufig","elliptic","method,","mesh" ], "intraHash" : "9db316fbe639db8fe7dbd32263b10ad6", "interHash" : "3b3eb9b7f23cb0657ebafecd547be4d8", "label" : "Graded mesh refinement and error estimates of higher order for DGFE\n\tsolutions of elliptic boundary value problems in polygons", "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","publisher":"Wiley Subscription Services, Inc., A Wiley Company", "year": "2012", "url": "http://dx.doi.org/10.1002/num.20668", "author": [ "Miloslav Feistauer","Anna-Margarete Sändig" ], "authors": [ {"first" : "Miloslav", "last" : "Feistauer"}, {"first" : "Anna-Margarete", "last" : "Sändig"} ], "volume": "28","number": "4","pages": "1124--1151","abstract": "Error estimates for DGFE solutions are well investigated if one assumes\n\tthat the exact solution is sufficiently regular. In this article,\n\twe consider a Dirichlet and a mixed boundary value problem for a\n\tlinear elliptic equation in a polygon. It is well known that the\n\tfirst derivatives of the solutions develop singularities near reentrant\n\tcorner points or points where the boundary conditions change. On\n\tthe basis of the regularity results formulated in Sobolev--Slobodetskii\n\tspaces and weighted spaces of Kondratiev type, we prove error estimates\n\tof higher order for DGFE solutions using a suitable graded mesh refinement\n\tnear boundary singular points. The main tools are as follows: regularity\n\tinvestigation for the exact solution relying on general results for\n\telliptic boundary value problems, error analysis for the interpolation\n\tin Sobolev--Slobodetskii spaces, and error estimates for DGFE solutions\n\ton special graded refined meshes combined with estimates in weighted\n\tSobolev spaces. Our main result is that there exist a local grading\n\tof the mesh and a piecewise interpolation by polynoms of higher degree\n\tsuch that we will get the same order O (ha) of approximation as in\n\tthe smooth case. � 2011 Wiley Periodicals, Inc. Numer Mehods Partial\n\tDifferential Eq, 2012", "issn" : "1098-2426", "doi" : "10.1002/num.20668", "bibtexKey": "feistauer2012graded" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/25a0ec547ae8701e6d99a32fd240925cb/hermann", "tags" : [ "problem;","{Collocation;","WEB-spline;","value","Boundary","Interpolation}" ], "intraHash" : "5a0ec547ae8701e6d99a32fd240925cb", "interHash" : "6372474b3d85063d9855b50a08467cb9", "label" : "Collocation with WEB-Splines", "user" : "hermann", "description" : "", "date" : "2017-05-18 11:32:12", "changeDate" : "2017-05-18 09:32:12", "count" : 1, "pub-type": "article", "journal": "ADVANCES IN COMPUTATIONAL MATHEMATICS","publisher":"SPRINGER","address":"233 SPRING ST, NEW YORK, NY 10013 USA", "year": "{2016}", "url": "", "author": [ "Christian Apprich","Klaus Hoellig","Joerg Hoerner","Ulrich Reif" ], "authors": [ {"first" : "Christian", "last" : "Apprich"}, {"first" : "Klaus", "last" : "Hoellig"}, {"first" : "Joerg", "last" : "Hoerner"}, {"first" : "Ulrich", "last" : "Reif"} ], "volume": "42","number": "4","pages": "823-842","abstract": "We describe a collocation method with weighted extended B-splines\n (WEB-splines) for arbitrary bounded multidimensional domains,\n considering Poisson's equation as a typical model problem. By slightly\n modifying the B-spline classification for the WEB-basis, the centers of\n the supports of inner B-splines can be used as collocation points. This\n resolves the mismatch between the number of basis functions and\n interpolation conditions, already present in classical univariate\n schemes, in a simple fashion. Collocation with WEB-splines is\n particularly easy to implement when the domain boundary can be\n represented as zero set of a weight function; sample programs are\n provided on the website http://www.web-spline.de. In contrast to\n standard finite element methods, no mesh generation and numerical\n integration is required, regardless of the geometric shape of the\n domain. As a consequence, the system equations can be compiled very\n efficiently. Moreover, numerical tests confirm that increasing the\n B-spline degree yields highly accurate approximations already on\n relatively coarse grids. Compared with Ritz-Galerkin methods, the\n observed convergence rates are decreased by 1 or 2 when using splines of\n odd or even order, respectively. This drawback, however, is outweighed\n by a substantially smaller bandwidth of collocation matrices.", "author-email" : "apprich@mathematik.uni-stuttgart.de\n hoellig@mathematik.uni-stuttgart.de\n hoerner@mathematik.uni-stuttgart.de\n reif@mathematik.tu-darmstadt.de", "eissn" : "1572-9044", "issn" : "1019-7168", "keywords-plus" : "ISOGEOMETRIC COLLOCATION; DIFFERENTIAL EQUATIONS; NURBS", "number-of-cited-references" : "38", "web-of-science-categories" : "Mathematics, Applied", "affiliation" : "Reif, U (Reprint Author), Tech Univ Darmstadt, AG Geometrie & Approximat, Schlossgartenstr 7, D-64289 Darmstadt, Germany.\n Apprich, Christian; Hoellig, Klaus; Hoerner, Joerg, Univ Stuttgart, IMNG, Fachbereich Math, Pfaffenwaldring 57, D-70569 Stuttgart, Germany.\n Reif, Ulrich, Tech Univ Darmstadt, AG Geometrie & Approximat, Schlossgartenstr 7, D-64289 Darmstadt, Germany.", "research-areas" : "Mathematics", "language" : "English", "times-cited" : "0", "doi" : "10.1007/s10444-015-9444-x", "bibtexKey": "ISI:000382000300003" } ] }