An efficient mass-conserved domain decomposition scheme for the nonlinear parabolic problem

摘要

In this paper, a mass conserved domain decomposition method is developed for solving the nonlinear parabolic equations with Dirichlet conditions. The domain decomposition is divided into multiple subdomains, two steps are used to solve the numerical solutions on each sub-domain at every time interval [t(n), t(n+1)]. In the first step, the interface fluxes are computed by local multi-points weighted average from the solutions. Secondly, the interior solutions are solved by the solution-flux coupled scheme. By some auxiliary lemmas and the Brouwer fixed point theorem, the existence, uniqueness and convergence of our scheme are analyzed in the discrete L-2-norm. Numerical experiments are performed to illustrate the result. (C) 2019 Elsevier B.V. All rights reserved.