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Superconvergence of finite element approximations to Maxwell's equations
Author(s) -
Monk Peter
Publication year - 1994
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.1690100611
Subject(s) - superconvergence , mathematics , finite element method , maxwell's equations , sobolev space , mathematical analysis , convergence (economics) , mixed finite element method , grid , extended finite element method , geometry , physics , economics , thermodynamics , economic growth
We study superconvergence of edge finite element approximations to the magnetostatic problem and to the time‐dependent Maxwell system. We show that in special discrete norms there is an increase of one power in the order of convergence of the finite element method compared to error estimates in standard Sobolev norms. Our results are restricted to an orthogonal grid in R 3 , but the grid may be nonuniform. © 1994 John Wiley & Sons, Inc.