A Petrov-Galerkin method with quadrature for elliptic boundary value problems |
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| Authors: | Bialecki B; Ganesh M; Mustapha K |
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| Institution: |
1 Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, CO 80401, USA 2 School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia 3 School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia
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| Abstract: | We propose and analyse a fully discrete Petrov–Galerkinmethod with quadrature, for solving second-order, variable coefficient,elliptic boundary value problems on rectangular domains. Inour scheme, the trial space consists of C2 splines of degreer  3, the test space consists of C0 splines of degree r –2, and we use composite (r – 1)-point Gauss quadrature.We show existence and uniqueness of the approximate solutionand establish optimal order error bounds in H2, H1 and L2 norms. |
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| Keywords: | elliptic boundary value problems Petrov– Galerkin method splines Gauss quadrature |
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