Abstract
We propose an asymptotic preserving nodal discretization of the hyperbolic heat equation, also known as the P 1 equation, on unstructured meshes in 2-D. This method, in diffusive regime, overcomes the problem of the inconsistent limit with diffusion, of classical multidimensional extensions of 1-D asymptotic preserving schemes, based on edge formulation. We provide both theoretical and numerical results.
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Buet, C., Després, B. & Franck, E. Design of asymptotic preserving finite volume schemes for the hyperbolic heat equation on unstructured meshes. Numer. Math. 122, 227–278 (2012). https://doi.org/10.1007/s00211-012-0457-9
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DOI: https://doi.org/10.1007/s00211-012-0457-9