Convergence of BDF2-Galerkin finite element scheme for cancer invasion model

Abstract

This article aims to determine the convergence and error bounds for the fully discrete solutions of the cancer invasion model using two-step backward difference scheme (BDF2) in time and Galerkin finite element approximation in space. The existence and uniqueness of a solution is affirmed. We establish error estimates with optimal order convergence rates for full discretization. Finally, some numerical tests are used to authenticate the scheme’s competency and accuracy.