Error analysis of multipoint flux domain decomposition methods for evolutionary diffusion problems
We study space and time discretizations for mixed formulations of parabolic problems. The spatial approximation is based on the multipoint flux mixed finite element method, which reduces to an efficient cell-centered pressure system on general grids, including triangles, quadrilaterals, tetrahedra, and hexahedra. The time integration is performed by using a domain decomposition time-splitting technique combined with multiterm fractional step diagonally implicit RungeKutta methods. The resulting scheme is unconditionally stable and computationally efficient, as it reduces the global system to a collection of uncoupled subdomain problems that can be solved in parallel without the need for Schwarz-type iteration. Convergence analysis for both the semidiscrete and fully discrete schemes is presented.
domain decomposition mixed finite element fractional step cell-centered finite difference multipoint flux approximation operator splitting