{"9db316fbe639db8fe7dbd32263b10ad6mhartmann":{"DOI":"10.1002/num.20668","ISBN":"","ISSN":"1098-2426","URL":"http://dx.doi.org/10.1002/num.20668","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","annote":"","author":[{"family":"Feistauer","given":"Miloslav"},{"family":"Sändig","given":"Anna-Margarete"}],"citation-label":"feistauer2012graded","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Numerical Methods for Partial Differential Equations","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2012"]],"literal":"2012"},"event-place":"","id":"9db316fbe639db8fe7dbd32263b10ad6mhartmann","interhash":"3b3eb9b7f23cb0657ebafecd547be4d8","intrahash":"9db316fbe639db8fe7dbd32263b10ad6","issue":"4","issued":{"date-parts":[["2012"]],"literal":"2012"},"keyword":"boundary Sobolev--Slobodetskii refinement, spaces, Galerkin problems, spaces graded Sobolev discontinuous value weighted vorlaeufig elliptic method, mesh","misc":{"issn":"1098-2426","doi":"10.1002/num.20668"},"note":"","number":"4","number-of-pages":"27","page":"1124--1151","page-first":"1124","publisher":"Wiley Subscription Services, Inc., A Wiley Company","publisher-place":"","status":"","title":"Graded mesh refinement and error estimates of higher order for DGFE\n\tsolutions of elliptic boundary value problems in polygons","type":"article-journal","username":"mhartmann","version":"","volume":"28"}}