Additive Schwarz algorithms for parabolic problems
The paper deals with the solution of systems of linear algebraic equations that arise from symmetric linear parabolic finite element problems. The additive Schwarz domain decomposition methods for parabolic differential equations is introduced and also the dependence of convergence rates of these algorithms on parameters of time step and space-mesh is considered. The resulting preconditioned linear system of equations is solved by the conjugate gradient method. The author analyzes the error caused by the conjugate gradient method, namely he proves the convergence and the error estimates. Additionally to the backward Euler method also the Crank-Nicolson scheme is considered. Finally, a numerical example is enclosed.
scientific article; zbMATH DE number 5527464