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On the p version of the finite element method in the presence of numerical integration
Author(s) -
Kim Chang Geun,
Suri Manil
Publication year - 1993
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.1690090602
Subject(s) - numerical integration , quadrature (astronomy) , finite element method , mathematics , norm (philosophy) , error analysis , tanh sinh quadrature , numerical analysis , gauss–kronrod quadrature formula , calculus (dental) , mathematical analysis , nyström method , integral equation , medicine , electrical engineering , dentistry , political science , law , engineering , physics , thermodynamics
We analyze the error in the p version of the finite element method when the effect of the quadrature error is taken into account. We extend some results by Banerjee and Suri [ Math. Comput. 59 , 1–20 (1992)] on the H 1 ‐norm error to the case of the error in the L 2 norm. We investigate three sources of quadrature error that can occur: the error due to the numerical integration of the right‐hand side, that due to nonconstant coefficients, and that due to the presence of mapped elements. Presented are various theoretical and computational examples regarding the sharpness of our results. In addition, we make a note on the use of numerical quadrature in conjunction with p ‐adaptive procedures and on the necessity of overintegration in the h version with linear elements, when the L 2 norm is of interest. © 1993 John Wiley & Sons, Inc.