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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"
         ],
         
         "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"

      }
,
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         "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"

      }
	  
   ]
}