Abstract
AbstractWe formulate a higher‐order (superconvergent) Petrov–Galerkin method by determining, using a finite‐difference 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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