Superconvergence analysis of two-grid FEM for Maxwell’s equations with a thermal effect

Abstract Based on two-grid algorithm, we develop the superconvergence analysis of fully-discrete scheme with the lowest-order Nedelec element and Crank–Nicolson scheme for the magneto-heat coupling model, which is also considered as Maxwell’s equations with a thermal effect. Then, main process of numerical analysis has two parts: On one hand, we utilize Newton-type Taylor expansion on superconvergent solutions for those nonlinear terms on coarse mesh, differing from the numerical solution, which makes our given two-grid method successful. On the other hand, we prove the solutions on the fine mesh to be higher accuracy by the postprocessing interpolation technique. Such a design is conducive to improving the computational accuracy in space and decreasing time consumption simultaneously. By employing the skill, we can obtain the convergent rate of O ( Δ t 2 + h 2 + H 3 ) , which means that the space mesh size should satisfy h = O ( H 3 2 ) . Finally, the numerical example is presented to verify the theoretical results.