A Two-Level Crank-Nicolson Difference Scheme and Its Richardson Extrapolation Methods for a Magneto-Thermo-Elasticity Model (Advances in Applied Mathematics and Mechanics, 2024)
This study is concerned with numerical solutions of a Magneto-Thermo-Elasticity (MTE) model via a combination of energy-conserving finite differencemethod (FDM) with Richardson extrapolation methods (REMs). Firstly, by introducing two auxiliary functions and using second-order centered FDM and Crank-Nicolsonmethod to approximate spatial and temporal derivatives, respectively, a two-levelenergy-conserving FDM is established for a MTE model. The priori estimation, solvability, and convergence are derived rigorously by using the discrete energy method.Secondly, to improve computational efficiency, a class of REMs are also designed byconstructing the symbolic expansion of numerical solutions. Finally, numerical resultsconfirm the efficiency of the proposed algorithms and the exactness of the theoreticalfindings.