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• W205243011 abstract "AbstractIt is well known that singularities in the solution of boundary value problems due to corners and edges of the domain lead to a reduction of the convergence order of the standard finite element method when quasi-uniform meshes are used. It is also well known that locally graded meshes are suited to recover the optimal convergence order. Less well known are the critical angles when mesh grading becomes necessary; it is not always the same but depends on the norm in which the error is estimated. In this paper, an overview of the results is given and lacking estimates are pointed out. Since the error estimates for optimal control problems are based on those for pure boundary value problems both cases are always considered.KeywordsElliptic partial differential equationFinite elementsA priori error estimatesMesh gradingOptimal controlMathematics Subject Classification (2010)49M2565N1565N3065N50" @default.
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• W205243011 date "2014-01-01" @default.
• W205243011 modified "2023-10-06" @default.
• W205243011 title "Graded Meshes in Optimal Control for Elliptic Partial Differential Equations: An Overview" @default.
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• W205243011 doi "https://doi.org/10.1007/978-3-319-05083-6_18" @default.
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