Galerkin/Runge–Kutta discretizations of nonlinear parabolic equations

摘要

Global error bounds are derived for full Galerkin/Runge–Kutta discretizations of nonlinear parabolic problems, including the evolution governed by the p-Laplacian with p⩾2. The analysis presented here is not based on linearization procedures, but on the fully nonlinear framework of logarithmic Lipschitz constants and an extended B-convergence theory. The global error is bounded in L2 by Δxr/2+Δtq, where r is the convergence order of the Galerkin method applied to the underlying stationary problem and q is the stiff order of the algebraically stable Runge–Kutta method.