The relation between primal and dual boundary conditions for hyperbolic systems of equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:401

Article

Nordstrom, Jan¹  Ghasemi, Fatemeh¹ 

[1] Linkoping Univ, Dept Math, Computat Math, SE-58183 Linkoping, Sweden

关键词: Hyperbolic systems;    Boundary conditions;    Primal problem;    Dual problem;    Well-posedness;    Dual consistency;   

DOI  :  10.1016/j.jcp.2019.109032

来源: Elsevier

【 摘 要 】

In this paper we study boundary conditions for linear hyperbolic systems of equations and the corresponding dual problem. In particular, we show that the primal and dual boundary conditions are related by a simple scaling relation. It is also shown that the weak dual problem can be derived directly from the weak primal problem. Based on the continuous analysis, we discretize and perform computations with a high-order finite difference scheme on summation- by-parts form with weak boundary conditions. It is shown that the results obtained in the continuous analysis lead directly to stability results for the primal and dual discrete problems. Numerical experiments corroborate the theoretical results. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free