An a Posteriori Error Estimator for a Non-Conforming Domain Decomposition Method for a Harmonic Elastodynamics Equation

Abstract

We develop a reliable residual-based a posteriori error estimator for a non-conforming method with non-matching meshes for a harmonic elastodynamics equation and show that the approximation method converges with an optimal order to the exact solution. Moreover, we propose an adaptive strategy to reduce computational cost and derive better approximations for problems with singularities and with large approximating systems. Numerical experiments confirm theoretical conclusions.