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• W2342296979 abstract "Consider the Poisson equation on a convex polygonal domain and the finite element method of degree $mgeq 1$ associated with a family of graded meshes for possible singular solutions. We prove the stability of the Ritz projection onto the finite element space in $W^1_p$, $1<pleq infty$. Consequently, we obtain finite element error estimates in $W^1_p$ for $1<pleq infty$ and in $L^p$ for $1<p<infty$. The key to the analysis is the use of the “index engineering” methodology in modified Kondrat$’$ev weighted spaces. We also mention possible extensions and applications of these results." @default.
• W2342296979 created "2016-06-24" @default.
• W2342296979 creator A5029413421 @default.
• W2342296979 date "2016-04-13" @default.
• W2342296979 modified "2023-10-17" @default.
• W2342296979 title "The $W^1_p$ stability of the Ritz projection on graded meshes" @default.
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• W2342296979 doi "https://doi.org/10.1090/mcom/3101" @default.
• W2342296979 hasPublicationYear "2016" @default.
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