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Some New Error Estimates for Ritz--Galerkin Methods with Minimal Regularity Assumptions

Authors:	Alfred H. Schatz Junping Wang.

Affiliation:	Department of Mathematics, Cornell University, Ithaca, New York 14853 ; Department of Mathematics, University of Wyoming, Laramie, Wyoming 82071

Abstract:	New uniform error estimates are established for finite element approximations of solutions of second-order elliptic equations using only the regularity assumption $\|u\|_1 leq c\|f\|_{-1}$ . Using an Aubin--Nitsche type duality argument we show for example that, for arbitrary (fixed) sufficiently small, there exists an such that for $begin{displaymath}\|u-u_h\|_0 leq varepsilon \|u-u_h\|_1. end{displaymath}$ Here, denotes the norm on the Sobolev space . Other related results are established.

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