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Penalty combinations of the Ritz-Galerkin and finite difference methods for singularity problems

✍ Scribed by Zi-Cai Li

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
694 KB
Volume
81
Category
Article
ISSN
0377-0427

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✦ Synopsis

Penalty combination of the Ritz~3alerkin and finite difference methods is presented for solving elliptic boundary value problems with singularities. The superconvergence rate, O(h2-~), of solution derivatives by the combination can be achieved while using quasiuniform rectangular difference grids, where h is the maximal mesh length of difference grids used ira the finite difference method, and 6( > 0) is an arbitrarily small number. It is due to its simplicity that the penalty combination of the Ritz-Galerkin and finite difference methods is highly recommended for solving the complicated problems with multiple singularities and multiple interfaces.

πŸ“œ SIMILAR VOLUMES

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This paper presents six combinations of the Ritz-Galerkin method and the finite difference method for solving elliptic boundary value problems. Not only optimal convergence rates of solutions but also superconvergence rates of solution derivatives can be achieved. The non-conforming combination and

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