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Numerical study of the HP version of mixed discontinuous finite element methods for reaction‐diffusion problems: The 1D case
Author(s) -
Chen Hongsen,
Chen Zhangxin,
Li Baoyan
Publication year - 2003
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.10063
Subject(s) - mathematics , degree of a polynomial , polynomial , convergence (economics) , finite element method , degree (music) , reaction–diffusion system , dimension (graph theory) , grid , space (punctuation) , numerical analysis , diffusion , partial differential equation , numerical stability , stability (learning theory) , mathematical analysis , geometry , pure mathematics , computer science , operating system , physics , machine learning , acoustics , economics , thermodynamics , economic growth
This article studies the stability and convergence of the hp version of the three families of mixed discontinuous finite element (MDFE) methods for the numerical solution of reaction‐diffusion problems. The focus of this article is on these problems for one space dimension. Error estimates are obtained explicitly in the grid size h , the polynomial degree p , and the solution regularity; arbitrary space grids and polynomial degree are allowed. These estimates are asymptotically optimal in both h and p for some of these methods. Extensive numerical results to show convergence rates in h and p of the MDFE methods are presented. Theoretical and numerical comparisons between the three families of MDFE methods are described. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 525–553, 2003