A posteriori error estimates for fully discrete schemes for the time dependent Stokes problem

被引：7

作者：

Baensch, E. ^{[1
]}

Karakatsani, F. ^{[2
]}

Makridakis, C. G. ^{[3
,4
,5
]}

机构：

[1] Appl Math III, Cauerstr 11, D-91058 Erlangen, Germany

[2] Univ Chester, Dept Math, Fac Sci & Engn, Thornton Sci Pk,Pool Lane, Chester CH2 4NU, Cheshire, England

[3] Univ Crete, DMAM, Modelling & Sc Comp, GR-70013 Iraklion, Greece

[4] FORTH, Inst Appl & Computat Math, GR-70013 Iraklion, Greece

[5] Univ Sussex, MPS, Brighton BN1 9QH, E Sussex, England

来源：

CALCOLO | 2018年 / 55卷 / 02期

基金：

欧盟地平线“2020”;

关键词：

A posteriori error estimators; Time dependent Stokes; Reconstruction; Adaptivity; Mesh change; Crouzeix-Raviart element; FINITE-ELEMENT APPROXIMATIONS; ELLIPTIC RECONSTRUCTION; MESH MODIFICATION; EQUATIONS;

D O I：

10.1007/s10092-018-0259-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work is devoted to a posteriori error analysis of fully discrete finite element approximations to the time dependent Stokes system. The space discretization is based on popular stable spaces, including Crouzeix-Raviart and Taylor-Hood finite element methods. Implicit Euler is applied for the time discretization. The finite element spaces are allowed to change with time steps and the projection steps include alternatives that is hoped to cope with possible numerical artifices and the loss of the discrete incompressibility of the schemes. The final estimates are of optimal order in L-infinity(L-2) for the velocity error.

引用

页数：32

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