Submitted

Optimal Rate of Convergence in $L^2$-Norm of An Adaptive Finite Element Method for Elliptic Equations

Long Chen

Submitted

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ABSTRACT:

 In this paper, an adaptive finite element algorithm to
control the error in $L^2$-norm is developed for second order elliptic
equations. It complements the standard adaptive finite element method
with a procedure to control the mesh size according to the a priori
information on the second derivative of the solution. Optimal rate of
convergence in $L^2$-norm is proved for convex domains in both two and
three domains and for polygonal domains in two dimensions.