数学
分段
非线性系统
变量(数学)
反向
应用数学
拉普拉斯算子
后向微分公式
数学分析
微分方程
几何学
常微分方程
物理
量子力学
搭配法
作者
Bosco García-Archilla,Julia Novo
出处
期刊:Ima Journal of Numerical Analysis
日期:2022-10-04
被引量:3
标识
DOI:10.1093/imanum/drac058
摘要
Abstract This paper studies fully discrete finite element approximations to the Navier–Stokes equations using inf-sup stable elements and grad-div stabilization. For the time integration, two implicit–explicit second-order backward differentiation formulae (BDF2) schemes are applied. In both, the Laplacian is implicit while the nonlinear term is explicit, in the first one, and semiimplicit, in the second one. The grad-div stabilization allows us to prove error bounds in which the constants are independent of inverse powers of the viscosity. Error bounds of order $r$ in space are obtained for the $L^2$ error of the velocity using piecewise polynomials of degree $r$ to approximate the velocity together with second-order bounds in time, both for fixed time-step methods and for methods with variable time steps. A Courant Friedrichs Lewy (CFL)-type condition is needed for the method in which the nonlinear term is explicit relating time-step and spatial mesh-size parameters.
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