Error analysis for full discretizations of quasilinear parabolic problems on evolving surfaces
Provides rigorous error analysis for numerical simulation of quasilinear parabolic problems on moving domains, important for applications in biology and fluid dynamics.
Proved optimal-order convergence for full discretizations of quasilinear parabolic PDEs on evolving surfaces using evolving surface finite elements and Runge-Kutta/BDF time integrators.
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 BDF time integrators, we obtain convergence results for the fully discrete problems.