Interior maximum-norm estimates for finite element methods. II

Schatz, A. H.; Wahlbin, L. B.

doi:10.1090/S0025-5718-1995-1297478-7

Interior maximum-norm estimates for finite element methods. II
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by A. H. Schatz and L. B. Wahlbin PDF

Math. Comp. 64 (1995), 907-928 Request permission

Abstract:

We consider bilinear forms $A( \bullet , \bullet )$ connected with second-order elliptic problems and assume that for ${u_h}$ in a finite element space ${S_h}$, we have $A(u - {u_h},\chi ) = F(\chi )$ for $\chi$ in ${S_h}$ with local compact support. We give local estimates for $u - {u_h}$ in ${L_\infty }$ and $W_\infty ^1$ of the type "local best approximation plus weak outside influences plus the local size of F".

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