Pointwise Error Estimates for Differences in Piecewise Linear Finite Element Approximations

Authors:
Alfred H. Schatz;Lars B. Wahlbin
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2003

Citing 0
Cited 2

Asymptotic Error Expansions for the Finite Element Method for Second Order Elliptic Problems in $R^N$, $N\geq2$. I: Local Interior Expansions

SIAM Journal on Numerical Analysis
Local A Posteriori Estimates on a Nonconvex Polygonal Domain

SIAM Journal on Numerical Analysis

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Abstract

We consider piecewise linear finite element approximations uh to u the solution of an elliptic boundary value problem. New estimates for the differences |e(x1)-e(x2)| (where e(x) = u(x)-u_h(x) is the error and x1 and x2 are any two points in the domain) are obtained in terms of weighted $L_\infty$ norms. As a consequence, so-called asymptotic expansion inequalities are derived that have been applied to obtain asymptotically exact a posteriori estimators for the gradient on each element.