一类完全非线性椭圆偏微分方程的最小残差离散化

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

IMA Journal of Numerical Analysis Pub Date : 2025-08-28 DOI:10.1093/imanum/draf075

Dietmar Gallistl, Ngoc Tien Tran

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引用次数: 0

摘要

本文介绍了求解一类椭圆型全非线性偏微分方程的有限元方法。它们基于基于亚历山德罗夫-贝克曼-普奇估计的最小残差原理。在相当一般的算子结构假设下，在$L^{^\infty} $范数下证明了$C^{1}$符合和不连续Galerkin方法的收敛性。对残差局部信息驱动的自适应网格细化在二维和三维空间的性能进行了数值实验。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Minimal residual discretization of a class of fully nonlinear elliptic PDE

This work introduces finite-element methods for a class of elliptic fully nonlinear partial differential equations. They are based on a minimal residual principle that builds upon the Alexandrov–Bakelman–Pucci estimate. Under rather general structural assumptions on the operator, convergence of $C^{1}$ conforming and discontinuous Galerkin methods is proven in the $L^{^\infty} $ norm. Numerical experiments on the performance of adaptive mesh refinement driven by local information of the residual in two and three space dimensions are provided.

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来源期刊

IMA Journal of Numerical Analysis 数学-应用数学

CiteScore

5.30

自引率

4.80%

发文量

审稿时长

6-12 weeks

期刊介绍： The IMA Journal of Numerical Analysis (IMAJNA) publishes original contributions to all fields of numerical analysis; articles will be accepted which treat the theory, development or use of practical algorithms and interactions between these aspects. Occasional survey articles are also published.