Gauss–Runge–Kutta time discretization of wave equations on evolving surfaces
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This paper is concerned with an error analysis for a full discretization of the linear wave equation on a moving surface. The equation is discretized in space by the evolving surface finite element method. Discretization in time is done by Gauß–Runge–Kutta (GRK) methods, aiming for higher-order accuracy in time and unconditional stability of the fully discrete scheme. The latter is established in the natural time-dependent norms by using the algebraic stability and the coercivity property of the GRK methods together with the properties of the spatial semi-discretization. Under sufficient regularity conditions, optimal-order error estimates for this class of fully discrete methods are shown. Numerical experiments are presented to confirm some of the theoretical results.
Mathematics Subject Classification (2000)65M12 65M15 65M60 35L99 35R01 35R37
The author would like to thank Christian Lubich for introducing him to the topic of this paper, for the fruitful discussions and insightful suggestions.
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