An efficient two-step explicit/Crank-Nicolson with finite element approach for three-dimensional coupled Burgers' equations with source terms

This paper constructs an efficient two-step explicit/Crank-Nicolson technique combined with finite element method to simulate a three-dimensional coupled Burgers equations with source terms, subject to appropriate initial and boundary conditions. The space derivatives are approximated using the finite element formulation whereas a combination of an efficient explicit scheme and crank-Nicolson approach is employed to interpolate the time derivative. The developed computational technique efficiently treats the time derivative term, ensuring its stability across small time steps. Both stability and convergence order of the new algorithm are numerically analyzed using the L^{\infty}(0,T;L^{2})-norm. The computational results suggest that the proposed two-step explicit/Crank-Nicolson approach is temporal second-order accurate and spatial third-order convergent. Four numerical examples are carried out to show the applicability and the efficiency of the new strategy. AMS Subject Classification (MSC): 65M12, 65M06.