Charles I. Goldstein

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We describe and analyze certain V-cycle multigrid algorithms with forms deened by numerical quadrature applied to the approximation of symmetric second order elliptic boundary value problems. This approach can be used for the eecient solution of nite element systems resulting from numerical quadrature as well as systems arising from nite diierence(More)
A finite element method is described for solving Helmholtz type boundary value problems in unbounded regions, including those with infinite boundaries. Typical examples include the propagation of acoustic or electromagnetic waves in waveguides. The radiation condition at infinity is based on separation of variables and differs from the classical Sommerfeld(More)
We analyze multigrid convergence rates when elliptic boundary value problems are discretized using finite element methods with numerical integration. The resulting discrete problem does not fall into the standard variational framework for analyzing multigrid methods since the bilinear forms on different grid levels are not suitably related to each other. We(More)
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