Mixed finite element algorithm for a nonlinear time fractional wave model

Abstract

In this article, a mixed element algorithm is presented to look for the numerical solution for a class of nonlinear wave model with the Caputo fractional derivative. By introducing two auxiliary functions and reducing order technique of fractional derivative, the studied model with high-order derivative in time is transformed into a coupled system including three lower order equations. Next, a fully discrete mixed element algorithm is formulated, where the temporal direction is approximated by a second-order scheme. The stability analysis of the proposed mixed scheme is done and optimal error estimates for three functions are derived. Finally, the numerical tests are carried out to verify the theory results.