Discretization error analysis for a radially symmetric harmonic map heat flow problem

IMA Journal of Numerical Analysis, vol. 46, pp. 1–20

Abstract

Abstract In this paper we study the harmonic map heat flow problem for a radially symmetric case. The corresponding partial differential equation plays a key role in many analyses of harmonic map heat flow problems. We consider a basic discretization method for this problem, namely a second-order finite difference discretization in space combined with a semi-implicit Euler method in time. The semi-implicit Euler method results in a linear problem at each time step. We restrict ourselves to the regime of smooth solutions of the continuous problem and present an error analysis of this discretization method. This results in optimal-order discretization error bounds (apart from a logarithmic term). We also present discrete energy estimates that mimic the decrease of the energy of the continuous solution.

Authors 1

1. Arnold Reusken corresponding Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik , RWTH-Aachen University, D-52056 Aachen, Germany