Finite element methods for Darcy’s problem coupled with the heat equation
Abstract
In this article, we study theoretically and numerically the heat equation coupled with Darcy’s law by a nonlinear viscosity depending on the temperature. We establish existence of a solution by using a Galerkin method and we prove uniqueness. We propose and analyze two numerical schemes based on finite element methods. An optimal a priori error estimate is then derived for each numerical scheme. Numerical experiments are presented that confirm the theoretical accuracy of the discretization.
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This paper has been published in Numer. Math., 139, (2018), pp. 315-348, doi 10.1007/s00211-017-0938-y