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Analysis of finite element approximation and quadrature of Volterra integral equations
Author(s) -
Bedivan Dana M.,
Fix George J.
Publication year - 1997
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/(sici)1098-2426(199711)13:6<663::aid-num4>3.0.co;2-p
Subject(s) - mathematics , quadrature (astronomy) , finite element method , stiffness matrix , gauss–kronrod quadrature formula , mathematical analysis , rate of convergence , galerkin method , mixed finite element method , gauss–jacobi quadrature , integral equation , nyström method , channel (broadcasting) , physics , electrical engineering , thermodynamics , engineering
In this article we study Galerkin finite element approximations to integral equations of the Volterra type. Our prime concern is the noncoercive case, which is not covered by the standard finite element theory. The question of rates of convergence is studied for the case where an exact stiffness matrix is available, as well as the case where the latter is approximated via quadrature rules. The optimality of these rules is also considered from the point of view of the effect the choice of the quadrature has on the overall rate of convergence. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 663–672, 1997