非线性抛物方程的自适应有限元算法

Adaptive Finite Element Algorithm for Nonlinear Parabolic Equations

本文讨论了一维空间中解非线性抛物方程的自适应有限元算法。对此非线性抛物方程,我们选择3层有限元格式,并以等分布原则为基础,对每一时间层选择非一致网格以保证误差具有较高的精度。此算法对大梯度的问题有较强的实用性。应用此算法的计算实例在文末给出。

We discussed an adaptive finite element algorithm for solving nonlinear parabolic equations in one-dimention. We presented a three-level finite element scheme for this equation, and needed equidistribute rule to choose non-uniform mesh for every time step in order to get a better convergence of error estimate. It is effective for Large-Gradient problems. Finally, we gave an example for using this algorithm.