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A mimetic Green element method
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DOI：10.1016/j.enganabound.2018.12.004.png)
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Abstract
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Green element method (GEM) is a numerical approach that combines boundary element method (BEM) and finite element method (FEM), which is effective to solve many physical problems, such as diffusion equation, heat transfer equation, etc. This paper proposes a novel GEM named mimetic GEM, which utilizes discrete flux operator derived from mimetic FDM to approximate boundary integral of the product of fundamental solution and edge-normal flux in GEM. Proposed mimetic GEM is indeed a novel numerical method mixing the ideas of BEM, FEM, and mimetic FDM, which The method synthesizes some typical advantages of traditional numerical methods, that has a semi-analytical accuracy same as BEM. The method can be adaptive to unstructured grid same as FEM, and has a good convergence same as FDM.
Keywords:
Green element method
Mimetic finite difference method
Boundary element method
Finite difference method
Finite element method
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