基于优化的符号变化椭圆 PDE 方法

A. Abdulle, Simon Lemaire
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引用次数: 0

摘要

我们研究椭圆型符号移动问题的数值逼近。我们全面分析和评估了 [Abdulle, Huber, Lemaire; CRAS, 17] 中简要介绍的方法。我们的方法基于域分解和优化。在对沿符号变化界面的精确法向通量轨迹进行额外的可整性假设后,我们的方法被证明是收敛的,只要在给定载荷下,PDE 存在唯一的有限能量解。与依赖于使用几何拟合网格族的 T-coercivity 方法不同,我们的方法适用于任意(符合界面要求的)网格序列。此外,我们还证明了 T-coercivity 方法不适用于的一类问题的收敛性。一套全面的测试案例补充了我们的分析。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An optimization-based method for sign-changing elliptic PDEs
We study the numerical approximation of sign-shifting problems of elliptic type. We fully analyze and assess the method briefly introduced in [Abdulle, Huber, Lemaire; CRAS, 17]. Our method is based on domain decomposition and optimization. Upon an extra integrability assumption on the exact normal flux trace along the sign-changing interface, our method is proved to be convergent as soon as, for a given loading, the PDE admits a unique solution of finite energy. Departing from the T-coercivity approach, which relies on the use of geometrically fitted mesh families, our method works for arbitrary (interface-compliant) mesh sequences. Moreover, it is shown convergent for a class of problems for which T-coercivity is not applicable. A comprehensive set of test-cases complements our analysis.
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