Error analysis for full discretizations of quasilinear parabolic problems on evolving surfaces

Kovács, Balázs and Power Guerra, Christian A. (2015) Error analysis for full discretizations of quasilinear parabolic problems on evolving surfaces. Numerical Methods for Partial Differential Equations, 32 (4). pp. 1200-1231. ISSN 1098-2426

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Abstract

Convergence results are shown for full discretizations of quasilinear parabolic partial differential equations on evolving surfaces. As a semidiscretization in space the evolving surface finite element method is considered, using a regularity result of a generalized Ritz map, optimal order error estimates for the spatial discretization is shown. Combining this with the stability results for Runge–Kutta and backward differentiation formulae time integrators, we obtain convergence results for the fully discrete problems.

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