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• W2121031654 abstract "We consider finite element methods for a model second-order elliptic equation on a general bounded convex polygonal or polyhedral domain. Our first main goal is to extend the best approximation property of the error in the $W^1_{infty }$ norm, which is known to hold on quasi-uniform meshes, to more general graded meshes. We accomplish it by a novel proof technique. This result holds under a condition on the grid which is mildly more restrictive than the shape regularity condition typically enforced in adaptive codes. The second main contribution of this work is a discussion of the properties of and relationships between similar mesh restrictions that have appeared in the literature." @default.
• W2121031654 created "2016-06-24" @default.
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• W2121031654 creator A5024056335 @default.
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• W2121031654 date "2011-09-29" @default.
• W2121031654 modified "2023-10-06" @default.
• W2121031654 title "Best approximation property in the $W^1_{infty }$ norm for finite element methods on graded meshes" @default.
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• W2121031654 doi "https://doi.org/10.1090/s0025-5718-2011-02546-9" @default.
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