| Abstract: | In this paper, we are concerned with the constrained finite element method
based on domain decomposition satisfying the discrete maximum principle for diffusion
problems with discontinuous coefficients on distorted meshes. The basic idea of
domain decomposition methods is used to deal with the discontinuous coefficients. To
get the information on the interface, we generalize the traditional Neumann-Neumann
method to the discontinuous diffusion tensors case. Then, the constrained finite element
method is used in each subdomain. Comparing with the method of using the
constrained finite element method on the global domain, the numerical experiments
show that not only the convergence order is improved, but also the nonlinear iteration
time is reduced remarkably in our method. |
