UNCONDITIONALLY OPTIMAL ERROR ESTIMATES OF A CRANK-NICOLSON GALERKIN METHOD FOR THE NONLINEAR THERMISTOR EQUATIONS

摘要

This paper focuses on unconditionally optimal error analysis of an uncoupled and linearized Crank-Nicolson Galerkin finite element method for the time-dependent nonlinear thermistor equations in d-dimensional space, d = 2,3. In our analysis,we split the error function into two parts, one from the spatial discretization and one from the temporal discretization, by introducing a corresponding time-discrete (elliptic) system. We present a rigorous analysis for the regularity of the solution of the time-discrete system and error estimates of the time discretization. With these estimates and the proved regularity, optimal error estimates of the fully discrete Crank-Nicolson Galerkin method are obtained unconditionally. Numerical results confirm our analysis and show the efficiency of the method.