A POSTERIORI ERROR ESTIMATES FOR A COUPLED WAVE SYSTEM WITH A LOCAL DAMPING

摘要

We study a finite element method applied to a system of coupled wave equations in a bounded smooth domain inR~d, d- 1,2,3, associated with a locally distributed damping function. We start with a spatially continuous finite element formulation allowing jump discontinuities in time. This approach yields, L_2(L_2) and L_∞(L_2), a posteriori error estimates in terms of weighted residuals of the system. The proof of the a posteriori error estimates is based on the strong stability estimates for the corresponding adjoint equations. Optimal convergence rates are derived upon the maximal available regularity of the exact solution and justified through numerical examples. Bibliography: 14 titles. Illustrations: 4 figures.