On Galerkin difference methods

JOURNAL OF COMPUTATIONAL PHYSICS

卷:313

Article

Banks, J. W.¹  Hagstrom, T.² 

[1] Rensselaer Polytech Inst, Dept Math Sci, Troy, NY 12180 USA

[2] So Methodist Univ, Dept Math, POB 750156, Dallas, TX 75275 USA

关键词: Difference methods;    Galerkin methods;    Initial-boundary value problems;   

DOI  :  10.1016/j.jcp.2016.02.042

来源: Elsevier

【 摘 要 】

Energy-stable difference methods for hyperbolic initial-boundary value problems are constructed using a Galerkin framework. The underlying basis functions are Lagrange functions associated with continuous piecewise polynomial approximation on a computational grid. Both theoretical and computational evidence shows that the resulting methods possess excellent dispersion properties. In the absence of boundaries the spectral radii of the operators for the first and second derivative matrices are bounded independent of discretization order. With boundaries the spectral radius of the first order derivative matrix appears to be bounded independent of discretization order, and grows only slowly with discretization order for problems in second-order form. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free