具有二次非线性的四阶半线性问题的后验误差控制

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-04-03 DOI:10.1137/23m1589852

Carsten Carstensen, Benedikt Gräßle, Neela Nataraj

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引用次数: 0

摘要

SIAM 数值分析期刊》第 62 卷第 2 期第 919-945 页，2024 年 4 月。摘要。针对两个具有三线性非线性和一般源的四阶半线性问题，对五种最低阶有限元方法进行了一般后验误差分析。准最优平滑器将源项扩展到离散试验空间，更重要的是，它修改了不可压缩二维 Navier-Stokes 方程和 von Kármán 方程的流函数涡度公式中的三线性项。这首次为莫雷、两个不连续 Galerkin、[math] 内部惩罚和弱超珀尔对称内部惩罚离散化的二维 Navier-Stokes 方程的流函数涡度公式提供了高效可靠的后验误差估计。

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A Posteriori Error Control for Fourth-Order Semilinear Problems with Quadratic Nonlinearity

SIAM Journal on Numerical Analysis, Volume 62, Issue 2, Page 919-945, April 2024.
Abstract. A general a posteriori error analysis applies to five lowest-order finite element methods for two fourth-order semilinear problems with trilinear nonlinearity and a general source. A quasi-optimal smoother extends the source term to the discrete trial space and, more important, modifies the trilinear term in the stream-function vorticity formulation of the incompressible two-dimensional Navier–Stokes equations and the von Kármán equations. This enables the first efficient and reliable a posteriori error estimates for the two-dimensional Navier–Stokes equations in the stream-function vorticity formulation for Morley, two discontinuous Galerkin, [math] interior penalty, and weakly overpenalized symmetric interior penalty discretizations with piecewise quadratic polynomials.

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.