Linearly implicit full discretization of surface evolution
For researchers in numerical analysis of surface evolution, this provides a stable and convergent full discretization framework, though it is an incremental extension of existing methods.
The paper studies stability and convergence of full discretizations for surface evolution equations, combining higher-order ESFEM with linearly implicit BDF methods, and proves stability without geometry-dependent bounds. Numerical examples confirm convergence.
Stability and convergence of full discretizations of various surface evolution equations are studied in this paper. The proposed discretization combines a higher-order evolving-surface finite element method (ESFEM) for space discretization with higher-order linearly implicit backward difference formulae (BDF) for time discretization. The stability of the full discretization is studied in the matrix--vector formulation of the numerical method. The geometry of the problem enters into the bounds of the consistency errors, but does not enter into the proof of stability. Numerical examples illustrate the convergence behaviour of the full discretization.