Conservative domain decomposition schemes for solving two-dimensional heat equations

Abstract

In this paper, by combining the operator splitting technique, a new mass-conserved domain decomposition method for two-dimensional heat equations is proposed. Along the each direction, the interface fluxes are first calculated from the explicit fluxes, then the sub-domain’s interior solutions are paralelly computed by the C–N implicit scheme. The scheme is stable under the condition $$r\le 2(\sqrt{6}-2)$$ and the corresponding convergence order of the scheme are given in $$L^2$$ -norm. Numerical results confirm the theoretical results.