{  
   "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/29db316fbe639db8fe7dbd32263b10ad6/mathematik",         
         "tags" : [
            "Galerkin","Sobolev","Sobolev-Slobodetskii","boundary","discontinuous","elliptic","from:mhartmann","graded","ians","mesh","method","problems","refinement","spaces","value","vorlaeufig","weighted"
         ],
         
         "intraHash" : "9db316fbe639db8fe7dbd32263b10ad6",
         "interHash" : "3b3eb9b7f23cb0657ebafecd547be4d8",
         "label" : "Graded mesh refinement and error estimates of higher order for DGFE solutions of elliptic boundary value problems in polygons",
         "user" : "mathematik",
         "description" : "",
         "date" : "2018-07-20 10:54:24",
         "changeDate" : "2023-04-18 09:45:21",
         "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\r\n\tthat the exact solution is sufficiently regular. In this article,\r\n\twe consider a Dirichlet and a mixed boundary value problem for a\r\n\tlinear elliptic equation in a polygon. It is well known that the\r\n\tfirst derivatives of the solutions develop singularities near reentrant\r\n\tcorner points or points where the boundary conditions change. On\r\n\tthe basis of the regularity results formulated in Sobolev--Slobodetskii\r\n\tspaces and weighted spaces of Kondratiev type, we prove error estimates\r\n\tof higher order for DGFE solutions using a suitable graded mesh refinement\r\n\tnear boundary singular points. The main tools are as follows: regularity\r\n\tinvestigation for the exact solution relying on general results for\r\n\telliptic boundary value problems, error analysis for the interpolation\r\n\tin Sobolev--Slobodetskii spaces, and error estimates for DGFE solutions\r\n\ton special graded refined meshes combined with estimates in weighted\r\n\tSobolev spaces. Our main result is that there exist a local grading\r\n\tof the mesh and a piecewise interpolation by polynoms of higher degree\r\n\tsuch that we will get the same order O (ha) of approximation as in\r\n\tthe smooth case. � 2011 Wiley Periodicals, Inc. Numer Mehods Partial\r\n\tDifferential Eq, 2012",
         "issn" : "1098-2426",
         
         "doi" : "10.1002/num.20668",
         
         "bibtexKey": "feistauer2012graded"

      }
	  
   ]
}