Convergence analysis for H1-Galerkin mixed finite element approximation of one nonlinear integro-differential model

In this paper we investigate H1-Galerkin mixed finite element approximation of one nonlinear integro-differential equation. This method possesses some advantages such as approximating the unknown function and its gradient simultaneously as well as the finite element spaces being free of LBB condition. A priori error estimates of the unknown function and its gradient are derived for both semi-discrete and fully discrete schemes. A numerical example is presented to illustrate the theoretical findings.