A Posteriori Error Estimate and Adaptive Algorithm of the Finite Element Method for Elastic Scattering From Anisotropic Media With Transparent Boundary Condition

ABSTRACT In this paper, we consider the transmission model of elastic waves, where the bounded elastic bodies are anisotropic. By utilizing the Dirichlet‐to‐Neumann operator to truncate the unbounded physical domain, we can solve the transmission problem via the finite element discretization in a bounded domain. To improve computational efficiency for non‐smooth boundaries, we establish a residual‐based a posteriori error estimate for the Dirichlet‐to‐Neumann finite element method and develop an adaptive algorithm. Numerical experiments demonstrate that the proposed adaptive algorithm can significantly improve the computational efficiency.