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         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/2a40683a8ca5ef9739a9c29982cd65259/elkepeter",         
         "tags" : [
            "iadm","Lebesgue","systems","hyperbolic","spaces","wirth"
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         "intraHash" : "a40683a8ca5ef9739a9c29982cd65259",
         "interHash" : "7f25941f6a1d02cc17fe27fb9e89104f",
         "label" : "Variable Lebesgue spaces and hyperbolic systems",
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         "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",
         
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         "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"
         ],
         
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         "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",
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         "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"

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         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/2a795baaf1eb095e7f7ab84a05f884ad8/mhartmann",         
         "tags" : [
            "a","Dirac","estimators,","error","finite","fractional","methods,","posteriori","adaptivity,","element","spaces","mass,","Sobolev","vorlaeufig"
         ],
         
         "intraHash" : "a795baaf1eb095e7f7ab84a05f884ad8",
         "interHash" : "fea501ed2a4ad0de2f63886c01491c60",
         "label" : "A posteriori error estimates with point sources in fractional sobolev\n\tspaces",
         "user" : "mhartmann",
         "description" : "",
         "date" : "2018-07-20 10:54:15",
         "changeDate" : "2018-07-20 08:54:15",
         "count" : 7,
         "pub-type": "article",
         "journal": "Numerical Methods for Partial Differential Equations",
         "year": "2017", 
         "url": "http://dx.doi.org/10.1002/num.22065", 
         
         "author": [ 
            "F. D. Gaspoz","P. Morin","A. Veeser"
         ],
         "authors": [
         	
            	{"first" : "F. D.",	"last" : "Gaspoz"},
            	{"first" : "P.",	"last" : "Morin"},
            	{"first" : "A.",	"last" : "Veeser"}
         ],
         "volume": "33","number": "4","pages": "1018--1042",
         "issn" : "1098-2426",
         
         "owner" : "langeras",
         
         "doi" : "10.1002/num.22065",
         
         "bibtexKey": "gaspoz2017posteriori"

      }
	  
   ]
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