Finite element method combined with time graded meshes for the time-fractional coupled Burgers’ equations

In this article, we develop a numerical method to solve the Caputo time-fractional coupled Burgers’ equations using the finite element method combined with the L1 formula on graded meshes. We specifically derive an extended discrete fractional Gr \(\ddot{\text {o}}\) $\ddot{\text{o}}$ nwall inequality to analyze numerical methods on graded meshes for time-fractional coupled equations. With the help of this inequality, we present the stability and the error estimate of the time semi-discrete scheme, and prove the error estimate of the fully discrete scheme. We present numerical experiments to confirm our theoretical results.