Dimension splitting for quasilinear parabolic equations
In the current paper, we derive a rigorous convergence analysis for a broad range of splitting schemes applied to abstract nonlinear evolution equations, including the Lie and Peaceman-Rachford splittings. The analysis is in particular applicable to (possibly degenerate) quasilinear parabolic problems and their dimension splittings. The abstract framework is based on the theory of maximal dissipat