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Projection methods for Dirichlet's problem in approximating polygonal domains with boundary-value corrections

Authors: James H. Bramble, Todd Dupont and Vidar Thomée
Journal: Math. Comp. 26 (1972), 869-879
MSC: Primary 65N30
MathSciNet review: 0343657
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Abstract: Consider Dirichlet's problem in a plane domain $ \Omega $ with smooth boundary $ \partial \Omega $. For the purpose of its approximate solution, an approximating domain $ {\Omega _h},0 < h \leqq 1$, with polygonal boundary $ \partial {\Omega _h}$ is introduced where the segments of $ \partial {\Omega _h}$ have length at most $ h$. A projection method introduced by Nitsche [6] is then applied on $ {\Omega _h}$ to give an approximate solution in a finite-dimensional subspace of functions $ {S_h}$, for instance a space of splines defined on a triangulation of $ {\Omega _h}$. The boundary terms in the bilinear form associated with Nitsche's method are modified to correct for the perturbation of the boundary.

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Article copyright: © Copyright 1972 American Mathematical Society

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