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

@article{Kovacs2015ErrorAF,
  title={Error analysis for full discretizations of quasilinear parabolic problems on evolving surfaces},
  author={Bal'azs Kov'acs and C. Guerra},
  journal={arXiv: Numerical Analysis},
  year={2015}
}
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. 

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