A priori error estimates for a coseismic slip optimal control problem

Abstract

This article presents an a priori error estimation for a finite element discretization applied to an optimal control problem governed by a mixed formulation for linear elasticity equations, where weak symmetry is imposed for the stress tensor. The optimal control is given by a discontinuity jump in displacements, representing the coseismic slip along a fault plane. Inferring the fault slip during an earthquake is crucial for understanding earthquake dynamics and improving seismic risk mitigation strategies, making this optimal control problem scientifically significant. We establish an a priori error estimate using appropriate finite element spaces for control and states. Our theoretical convergence rates were validated through numerical experiments.