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Error Estimation of the Besse Relaxation Scheme for a Semilinear Heat Equation

Research paper by Georgios E. Zouraris

Indexed on: 21 Dec '18Published on: 21 Dec '18Published in: arXiv - Mathematics - Numerical Analysis



Abstract

The solution to the initial and Dirichlet boundary value problem for a semilinear, one dimensional heat equation is approximated by a numerical method that combines the Besse relaxation scheme in time (C. R. Acad. Sci. Paris S{\'e}r. I, vol. 326 (1998)) with a central finite difference method in space. A new, composite stability argument is developed, leading to an optimal, second-order error estimate in the discrete $L_t^{\infty}(H_x^1)-$norm. It is the first time in the literature where an error estimate for fully discrete approximations based on the Besse relaxation scheme is provided.