A mixed finite element method for solving coupled wave equation of Kirchhoff type with nonlinear boundary damping and memory term

Abstract

This paper is concerned with the numerical approximation of the solution of the coupled wave equation of Kirchhoff type with nonlinear boundary damping and memory term using a mixed finite element method. The Raviart‐Thomas mixed finite element method is one of the most prominent techniques to discretize the second‐order wave equations; therefore, we apply this scheme for space discretization. Furthermore, an L2‐in‐space error estimate is presented for this mixed finite element approximation. Finally, the efficiency of the method is verified by a numerical example.