An Adaptive Discrete Geometric Approach for high-accuracy solutions of 2-D elliptic problems on the coarse grid

Abstract

An Adaptive Discrete Geometric Approach is proposed for high-accuracy simulations of 2-D elliptic problems on the coarse grid. The idea is to reduce the error coming from the discretization of the constitutive equations by using the patch recovery technique. The integration-oriented scheme is adopted for the recovery procedure due to the high-precision of the regression functions. The accuracy and efficiency of the proposed approach are verified by the numerical tests.

Keywords

Discrete Geometric Approach patch recovery bicubic spline interpolation constitutive matrix

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