High-order methods for parabolic problems

Abstract

Error estimates valid for all t ⩾ 0 for the semi-discrete Galerkin approximation of a parabolic mixed boundary-initial value problem are presented. The solution of the resulting system of ordinary differential equations by implicit Runge-Kutta formulae for arbitrarily high order of accuracy, are discussed. Strongly A-stable methods are found to be advantageous. Theoretical and experimental results for the solution of the resulting system of algebraic equations using a preconditioned outer iteration scheme are discussed. Even the inner linear algebraic equations are preferably solved by iteration.