Superconvergence Analysis Of Two-grid FEM For Maxwell’s Equations

This paper mainly studies two problems:Firstly,we develop the superconvergence analysis of two-grid method by Crank-Nicolson discrete scheme with the lowest Nedelec element for the magneto-heat coupling model.Our main contribution will have two parts.On one hand,in order to overcome the difficulty of misconvergence of classical two-grid method by the lowest Nedelec ele-ment,we employ the Newton-type Taylor expansion at the superconvergent solutions for the nonlinear terms on coarse mesh,which is different from the numerical solution on the coarse mesh classically.On the other hand,we push the two-grid solution to high accuracy by the postprocessing interpolation technique.The design can improve the computational accuracy in space and decrease time consumption simulta.neously.Based on this design,we can obtain the convergent rate O(Δt2+h2+H3),which means that the space mesh size satisfies h=O(H3/2).We also present one example to verify our theorem.Then,we give two-grid method and convergence analysis of the magnetized ferrite model.Firstly,we solved the source problem on coarse mesh.Then,we take a super-convergent solution on the coarse mesh into the equivalent problem on fine mesh as one correction.We use the Crank-Nicolson discrete scheme to obtain the convergent rate O(Δt2+h+H2).Finally,we give a numerical example,which illustrate that the method can improve the computational efficiency.