Solving Poisson equation with Robin boundary condition on a curvilinear mesh using high order mimetic discretization methods

This paper introduces a new software package, written in MATLAB®, that generates an extended discrete Laplacian (L=DG=∇⋅∇) based on the Castillo-Grone Mimetic difference operators over a general curvilinear grid. The boundary conditions are included in the extended discrete Laplacian Operator, i.e. Dirichlet, Neumann, as well as Robin boundary conditions. The user only needs to provide a curvilinear grid, a desired operator order, and the degree of the interpolating polynomial. The operator is tested in different condition and its performance is reported. Finally, based on accuracy of the results, amount of required memory, and the computation that is needed, it is concluded that the 4th order operator is the best one.