A Petrov–Galerkin method with quadrature for elliptic boundary value problems
نویسنده
چکیده
We propose and analyse a fully discrete Petrov–Galerkin method with quadrature, for solving second-order, variable coefficient, elliptic boundary value problems on rectangular domains. In our scheme, the trial space consists of C2 splines of degree r 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 solution and establish optimal order error bounds in H2, H1 and L2 norms.
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