SEMI-IMPLICIT APPROXIMATION OF WAVE MAPS INTO SMOOTH OR CONVEX SURFACES

摘要

A semi-implicit scheme using linear finite elements for the approximation of wave maps into smooth or convex surfaces is devised, and its stability is analyzed. Convergence is established for the case of the unit sphere as a target manifold, which is unconditional in the case of (2 + 1) Minkowski space. Numerical experiments illustrate the theoretical results.