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 dissipative operators, and we both give a summary of the used theory and some extensions of the classical results. The derived convergence results are illustrated by numerical experiments.

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