论文标题
堕胎抛物线方程家族的完全离散的有限元近似
Fully discrete finite element approximation for a family of degenerate parabolic mixed equations
论文作者
论文摘要
这项工作的目的是展示一个抽象框架，以通过在空间中使用有限元方法和及时的向后欧拉人方案分析线性退化抛物线混合方程的数值近似。我们认为足够的条件可以证明完全存在的问题具有独特的解决方案，并证明了近似值的准最佳误差估计。此外，我们表明，可以分析由动态流体（时间依赖的Stokes问题）和电磁应用（涡流模型）引起的混合有限元配方，可以分析为已发达理论的应用。最后，我们包括数值测试，以说明该方法的性能并确认理论结果。
The aim of this work is to show an abstract framework to analyze the numerical approximation for a family of linear degenerate parabolic mixed equations by using a finite element method in space and a Backward-Euler scheme in time. We consider sufficient conditions to prove that the fully-discrete problem has a unique solution and prove quasi-optimal error estimates for the approximation. Furthermore, we show that mixed finite element formulations arising from dynamics fluids (time-dependent Stokes problem) and from electromagnetic applications (eddy current models), can be analyzed as applications of the developed theory. Finally, we include numerical tests to illustrate the performance of the method and confirm the theoretical results.
