Support Operator Method for Laplace Equation on Unstructured Triangular Grid

Victor Ganzha, Richard Liska, Mikhail Shashkov, Christoph Zenger


A finite difference algorithm for solution of generalized Laplace equation on unstructured triangular grid is constructed by a support operator method. The support operator method first constructs discrete divergence operator from the divergence theorem and then constructs discrete gradient operator as the adjoint operator of the divergence. The adjointness of the operators is based on the continuum Green formulas which remain valid also for discrete operators. Developed method is exact for linear solution and has second order convergence rate. It is working well for discontinuous diffusion coefficient and very rough or very distorted grids which appear quite often e.~g. in Lagrangian simulations. Being formulated on the unstructured grid the method can be used on the region of arbitrary geometry shape. Numerical results confirm these properties of the developed method.


Mimetric finite difference; Laplace equation; unstructured triangular grid.

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