ANALYSIS OF A SPACE-TIME HYBRIDIZABLE DISCONTINUOUS GALERKIN METHOD FOR THE ADVECTION-DIFFUSION PROBLEM ON TIME-DEPENDENT DOMAINS

被引：7

作者：

Kirk, K. L. A. ^{[1
]}

Horvath, T. L. ^{[1
]}

Cesmelioglu, A. ^{[2
]}

Rhebergen, S. ^{[1
]}

机构：

[1] Univ Waterloo, Dept Appl Math, Waterloo, ON N2L 3G1, Canada

[2] Oakland Univ, Dept Math & Stat, Rochester, MI 48309 USA

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2019年 / 57卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

space-time; hybridized; discontinuous Galerkin; advection-diffusion equations; time-dependent domains; FINITE-ELEMENT-METHOD; NAVIER-STOKES EQUATIONS;

D O I：

10.1137/18M1202049

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents the first analysis of a space-time hybridizable discontinuous Galerkin method for the advection-diffusion problem on time-dependent domains. The analysis is based on nonstandard local trace and inverse inequalities that are anisotropic in the spatial and time-steps. We prove well-posedness of the discrete problem and provide a priori error estimates in a mesh-dependent norm. Convergence theory is validated by a numerical example solving the advection-diffusion problem on a time-dependent domain for approximations of various polynomial degrees.

引用

页码：1677 / 1696

页数：20

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