H. Esqueda, R. Herrera, S. Botello, C. Valero
We present a local formulation for 2D Discrete Exterior Calculus (DEC) similar to that of the Finite Element Method (FEM), which allows a natural treatment of material heterogeneity (assigning material properties element by element). It also allows us to deduce, in a principled manner, anisotropic fluxes and the DEC discretization of the pullback of 1-forms by the anisotropy tensor, i.e. we deduce the the discrete action of the anisotropy tensor on primal 1-forms. Due to the local formulation, the computational cost of DEC is similar to that of the Finite Element Method with Linear interpolating functions (FEML). The numerical DEC solutions to the anisotropic Poisson equation show numerical convergence, are very close to those of FEML on fine meshes and are slightly better than those of FEML on coarse meshes.
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Published on 19/06/20Accepted on 24/05/20Submitted on 22/04/20
Volume 36, Issue 2, 2020DOI: 10.23967/j.rimni.2020.05.003Licence: CC BY-NC-SA license
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