论文标题
一个堕胎抛物线问题家族的全差异有限元近似
Fully-discrete finite element approximation for a family of degenerate parabolic problems
论文作者
论文摘要
这项工作的目的是展示一个抽象框架，以在空间中使用有限元方法和在堕胎抛物线问题家族的家庭中使用有限元方法分析数值近似。我们推断出足够的条件，以确保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。最后，我们显示了一个退化的抛物线问题，该问题是由电磁应用引起的，并通过使用已发达的抽象理论推断出其适应性和收敛性，包括数值测试来说明该方法的性能并确认理论结果。关键字：抛物线退化方程，抛物线 - 纤维化方程，有限元方法，向后的Euler方案，完全差异近似，错误估计，涡流电流模型。
The aim of this work is to show an abstract framework to analyze the numerical approximation by using a finite element method in space and a Backward-Euler scheme in time of a family of degenerate parabolic problems. We deduce sufficient conditions to ensure that the fully-discrete problem has a unique solution and to prove quasi-optimal error estimates for the approximation. Finally, we show a degenerate parabolic problem which arises from electromagnetic applications and deduce its well-posedness and convergence by using the developed abstract theory, including numerical tests to illustrate the performance of the method and confirm the theoretical results. Keywords: parabolic degenerate equations, parabolic-elliptic equations, finite element method, backward Euler scheme, fully-discrete approximation, error estimates, eddy current model.
