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A higher-order accurate Petrov-Galerkin finite-element method for elliptic boundary-value problems

✍ Scribed by MacKinnon, R. J. ;Johnson, R. W. ;Langerman, M. A.

Publisher
Wiley (John Wiley & Sons)
Year
1992
Tongue
English
Weight
311 KB
Volume
8
Category
Article
ISSN
0748-8025

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✦ Synopsis

We formulate a higher-order (superconvergent) Petrov-Galerkin method by determining, using a finitedifference approximation, the optimal selection of quadratic and cubic modifications to the standard linear test function for bilinear elements. Application of this method to linear elliptic problems results in improved accuracy and higher rates of convergence for problems with constant coefficients and improved accuracy for problems with variable coefficients. Supporting numerical examples are given.

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