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• W2949873669 abstract "We develop a constructive piecewise polynomial approximation theory in weighted Sobolev spaces with Muckenhoupt weights for any polynomial degree. The main ingredients to derive optimal error estimates for an averaged Taylor polynomial are a suitable weighted Poincare inequality, a cancellation property and a simple induction argument. We also construct a quasi-interpolation operator, built on local averages over stars, which is well defined for functions in $L^1$. We derive optimal error estimates for any polynomial degree on simplicial shape regular meshes. On rectangular meshes, these estimates are valid under the condition that neighboring elements have comparable size, which yields optimal anisotropic error estimates over $n$-rectangular domains. The interpolation theory extends to cases when the error and function regularity require different weights. We conclude with three applications: nonuniform elliptic boundary value problems, elliptic problems with singular sources, and fractional powers of elliptic operators." @default.
• W2949873669 created "2019-06-27" @default.
• W2949873669 creator A5028288239 @default.
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• W2949873669 date "2014-02-09" @default.
• W2949873669 modified "2023-09-27" @default.
• W2949873669 title "Piecewise polynomial interpolation in Muckenhoupt weighted Sobolev spaces and applications" @default.
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• W2949873669 hasPublicationYear "2014" @default.
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