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Mathematics of Computation

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On the convergence rate of the cell discretization algorithm for solving elliptic problems

Authors: Maria Cayco, Leslie Foster and Howard Swann
Journal: Math. Comp. 64 (1995), 1397-1419
MSC: Primary 65N30
MathSciNet review: 1297464
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Abstract: Error estimates for the cell discretization algorithm are obtained for polynomial bases used to approximate both $ {H^k}(\Omega )$ and analytic solutions to selfadjoint elliptic problems. The polynomial implementation of this algorithm can be viewed as a nonconforming version of the h-p finite element method that also can produce the continuous approximations of the h-p method. The examples provided by our experiments provide discontinuous approximations that have errors similar to the finite element results.

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Keywords: Elliptic equations, finite element methods, hybrid methods, nonconforming methods, Lagrange multipliers, domain decomposition, cell discretization
Article copyright: © Copyright 1995 American Mathematical Society