A minimum Sobolev norm technique for the numerical discretization of PDEs

JOURNAL OF COMPUTATIONAL PHYSICS

卷:299

Article

Chandrasekaran, S.¹  Mhaskar, H. N.^2,3 

[1] Univ Calif Santa Barbara, Dept Elect & Comp Engn, Santa Barbara, CA 93106 USA

[2] CALTECH, Dept Math, Pasadena, CA 91125 USA

[3] Claremont Grad Univ, Inst Math Sci, Claremont, CA 91711 USA

关键词: Minimum Sobolev norm;    Golomb-Weinberger;    First-order PDEs;   

DOI  :  10.1016/j.jcp.2015.07.025

来源: Elsevier

【 摘 要 】

Partial differential equations (PDEs) are discretized into an under-determined system of equations and a minimum Sobolev norm solution is shown to be efficient to compute and converge under very generic conditions. Numerical results of a single code, that can handle PDEs in first-order form on complicated polygonal geometries, are shown for a variety of PDEs: variable coefficient div-curl, scalar elliptic PDEs, elasticity equation, stationary linearized Navier-Stokes, scalar fourth-order elliptic PDEs, telegrapher's equations, singular PDEs, etc. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free