Domain decomposition and splitting methods for mortar mixed finite element approximations to parabolic equations
The method considered in this paper combines the mortar mixed finite element domain decomposition spatial discretization with projection schemes for the time discretization, in order to obtain a fully parallel algorithm for parabolic equations. This method enables also the use of hybrid meshes and local time stepping. Two versions of the time discretization by operator splitting are presented. For both schemes unconditional stability is proved and for the incremental version convergence holds true if the condition \( O ( \Delta t / h^{1/2 }) \) is true. The main advantage of this method is to be fully parallel. A numerical example with well-known exact solution is presented and the convergence history of the error in \(L_2(\Omega)\) norm for the incremental scheme is involved.
scientific article; zbMATH DE number 1837411