A high-order discontinuous Galerkin approximation to ordinary differential equations with applications to elastodynamics

被引：18

作者：

Antonietti, Paola F. ^{[1
]}

Mazzieri, Ilario ^{[1
]}

Dal Santo, Niccolo ^{[2
]}

Quarteroni, Alfio ^{[2
]}

机构：

[1] Politecn Milan, MOX Lab Modeling & Sci Comp, Dept Math, Pza Leonardo da Vinci 32, I-20133 Milan, Italy

[2] Ecole Polytech Fed Lausanne, CMCS, Stn 8, CH-1015 Lausanne, Switzerland

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2018年 / 38卷 / 04期

关键词：

space-time finite elements; discontinuous Galerkin methods; second-order hyperbolic equations; FINITE-ELEMENT METHODS; FORMULATIONS; STABILITY;

D O I：

10.1093/imanum/drx062

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this work is to propose and analyse a new high-order discontinuous Galerkin finite element method for the time integration of a Cauchy problem for second-order ordinary differential equations. These equations typically arise after space semidiscretization of second-order hyperbolic-type differential problems, e.g., wave, elastodynamics and acoustics equations. After introducing the new method, we analyse its well-posedness and prove a priori error estimates in a suitable (mesh-dependent) norm. Numerical results are also presented to verify our theoretical estimates.

引用

页码：1709 / 1734

页数：26

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