Time-discrete higher order ALE formulations: a priori error analysis

被引：12

作者：

Bonito, Andrea ^{[1
]}

Kyza, Irene ^{[2
]}

Nochetto, Ricardo H. ^{[3
,4
]}

机构：

[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

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

[3] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[4] Univ Maryland, Inst Phys Sci & Technol, College Pk, MD 20742 USA

来源：

NUMERISCHE MATHEMATIK | 2013年 / 125卷 / 02期

基金：

美国国家科学基金会;

关键词：

CONVECTION-DIFFUSION EQUATION; GEOMETRIC CONSERVATION LAW; PARABOLIC EQUATIONS; STABILITY; SCHEMES;

D O I：

10.1007/s00211-013-0539-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive optimal a priori error estimates for discontinuous Galerkin (dG) time discrete schemes of any order applied to an advection-diffusion model defined on moving domains and written in the Arbitrary Lagrangian Eulerian (ALE) framework. Our estimates hold without any restrictions on the time steps for dG with exact integration or Reynolds' quadrature. They involve a mild restriction on the time steps for the practical Runge-Kutta-Radau methods of any order. The key ingredients are the stability results shown earlier in Bonito et al. (Time-discrete higher order ALE formulations: stability, 2013) along with a novel ALE projection. Numerical experiments illustrate and complement our theoretical results.

引用

页码：225 / 257

页数：33

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