A robust finite element method for nonhomogeneous Dirichlet problems in domains with curved boundaries

Bramble, James H.; King, J. Thomas

doi:10.1090/S0025-5718-1994-1242055-6

A robust finite element method for nonhomogeneous Dirichlet problems in domains with curved boundaries
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by James H. Bramble and J. Thomas King PDF

Math. Comp. 63 (1994), 1-17 Request permission

Abstract:

In this paper we consider a simple finite element method on an approximate polygonal domain using linear elements. The Dirichlet data are transferred in a natural way and the resulting linear system can be solved using multigrid techniques. Our analysis takes into account the change in domain and data transfer, and optimal-error estimates are obtained that are robust in the regularity of the boundary data provided they are at least square integrable. It is proved that the natural extension of our finite element approximation to the original domain is optimal-order accurate.

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