A Constrained Finite Element Method Based on Domain Decomposition Satisfying the Discrete Maximum Principle for Diffusion Problems (Communications in Computational Physics, 2018)
In this paper, we are concerned with the constrained finite element methodbased on domain decomposition satisfying the discrete maximum principle for diffusionproblems with discontinuous coefficients on distorted meshes. The basic idea ofdomain decomposition methods is used to deal with the discontinuous coefficients. Toget the information on the interface, we generalize the traditional Neumann-Neumannmethod to the discontinuous diffusion tensors case. Then, the constrained finite elementmethod is used in each subdomain. Comparing with the method of using theconstrained finite element method on the global domain, the numerical experimentsshow that not only the convergence order is improved, but also the nonlinear iterationtime is reduced remarkably in our method.