Additive Schwarz algorithms for parabolic problems

In this paper, we consider the solution of linear systems of algebraic equations that arise from parabolic finite element problems. We introduce additive Schwarz domain decomposition methods for parabolic differential equations and also consider the dependence of convergence rates of these algorithms on parameters of time step and space-mesh. The resulting preconditioned linear system of equations is solved by the conjugate gradient method. Finally we give a numerical example.