Piecewise polynomial approximation of a nonlocal phase transitions model

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:420

Article

Bhowmik, Samir Kumar

关键词: Finite element method;    Phase transitions;    Quadrature;    Collocations;    Error analysis;   

DOI  :  10.1016/j.jmaa.2014.06.040

来源: Elsevier

【 摘 要 】

Piecewise collocation-finite element and Galerkin-finite element methods are proposed and analysed for a nonlinear partial integro-differential equation that arises in the modeling of phase transitions. We compute solutions in both methods using some standard quadrature rules. We present the order of accuracy of such semidiscrete time dependent problem with full integral and quadrature for the Galerkin inner product considering both the real solutions and the approximate solutions are sufficiently smooth in whole domain Omega. We also find an upper bound considering the approximate solutions are L-2 in Omega and H-s in each subdomain w(i) such that Omega = boolean OR(i) w(i). (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free