hp-adaptive discontinuous Galerkin methods for non-stationary convection-diffusion problems

被引：7

作者：

Cangiani, A. ^{[1
,6
]}

Georgoulis, E. H. ^{[1
,2
,3
]}

Giani, S. ^{[5
]}

Metcalfe, S. ^{[4
]}

机构：

[1] Univ Leicester, Dept Math, Univ Rd, Leicester LE1 7RH, Leics, England

[2] Natl Tech Univ Athens, Sch Appl Math & Phys Sci, Dept Math, Zografos 15780, Greece

[3] Fdn Res & Technol Hellas, Inst Appl & Computat Math, Iraklion 70013, Greece

[4] Univ York, Dept Chem, York YO10 5DD, N Yorkshire, England

[5] Durham Univ Lower Mountjoy, Dept Engn, South Rd, Durham DH1 3LE, England

[6] Sch Math Sci, Univ Pk, Nottingham NG7 2RD, England

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2019年 / 78卷 / 09期

基金：

英国工程与自然科学研究理事会;

关键词：

Discontinuous Galerkin; Unsteady convection-diffusion; A posteriori error estimation; Adaptive finite element methods; Anisotropic meshes; POSTERIORI ERROR ESTIMATION; ELLIPTIC RECONSTRUCTION; MESH MODIFICATION; APPROXIMATIONS; ESTIMATOR;

D O I：

10.1016/j.camwa.2019.04.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An a posteriori error estimator for the error in the (L-2(H-1) + L-infinity(L-2))-type norm for an interior penalty discontinuous Galerkin (dG) spatial discretisation and backward Euler temporal discretisation of linear non-stationary convection-diffusion initial/boundary value problems is derived, allowing for anisotropic elements. The proposed error estimator is used to drive an hp-space-time adaptive algorithm wherein directional mesh refinement is employed to give rise to highly anisotropic elements able to accurately capture layers. The performance of the hp-space-time adaptive algorithm is assessed via a number of standard test problems characterised by sharp and/or moving layers. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页码：3090 / 3104

页数：15

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