Superconvergent functional output for time-dependent problems using finite differences on summation-by-parts form

JOURNAL OF COMPUTATIONAL PHYSICS

卷:231

Article

Berg, Jens¹  Nordstrom, Jan² 

[1] Uppsala Univ, Dept Informat Technol, Div Comp Sci, SE-75105 Uppsala, Sweden

[2] Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden

关键词: High order finite differences;    Summation-by-parts;    Superconvergence;    Time-dependent functional output;    Dual consistency;    Stability;   

DOI  :  10.1016/j.jcp.2012.06.032

来源: Elsevier

【 摘 要 】

Finite difference operators satisfying the summation-by-parts (SBP) rules can be used to obtain high order accurate, energy stable schemes for time-dependent partial differential equations, when the boundary conditions are imposed weakly by the simultaneous approximation term (SAT). In general, an SBP-SAT discretization is accurate of order p + 1 with an internal accuracy of 2p and a boundary accuracy of p. Despite this, it is shown in this paper that any linear functional computed from the time-dependent solution, will be accurate of order 2p when the boundary terms are imposed in a stable and dual consistent way. The method does not involve the solution of the dual equations, and superconvergent functionals are obtained at no extra computational cost. Four representative model problems are analyzed in terms of convergence and errors, and it is shown in a systematic way how to derive schemes which gives superconvergent functional outputs. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free