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- W2066322206 abstract "We study the approximation properties of some general finite-elementspaces constructed using improved graded meshes. In our results,either the approximating function or the function to be approximated(or both) are in a weighted Sobolev space. We consider also the$L^p$-version of these spaces. The finite-element spaces that wedefine are obtained from {em conformally invariant} families offinite elements (no affine invariance is used), stressing the use ofelements that lead to higher regularity finite-element spaces. Weprove that for a suitable grading of the meshes, one obtains the usualoptimal approximation results. We provide a construction of thesespaces that does not lead to long, ``skinny'' triangles. Our resultsare then used to obtain $L^2$ error estimates and $h^m$-quasi-optimalrates of convergence for the FEM approximation of solutions ofstrongly elliptic interface/boundary value problems." @default.
- W2066322206 created "2016-06-24" @default.
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- W2066322206 creator A5080524039 @default.
- W2066322206 date "2015-02-26" @default.
- W2066322206 modified "2023-09-25" @default.
- W2066322206 title "Graded mesh approximation in weighted Sobolev spaces and elliptic equations in 2D" @default.
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- W2066322206 doi "https://doi.org/10.1090/s0025-5718-2015-02934-2" @default.
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