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Improved error estimates for mixed finite‐element approximations for nonlinear parabolic equations: The continuous‐time case
Author(s) -
Garcia Sonia M. F.
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.1690100202
Subject(s) - mathematics , finite element method , nonlinear system , mixed finite element method , mathematical analysis , element (criminal law) , physics , quantum mechanics , thermodynamics , political science , law
L 2 ‐error estimates are computed for mixed finite‐element methods for second‐order quasilinear (and linear, variable coefficient) parabolic equations. Results are given for the continuous‐time case. The convergence of the values for both the scalar function and the flux is demonstrated. The technique used here covers the lowest‐order Raviart‐Thomas spaces, as well as the higher‐order spaces. A second paper will present the analysis of a fully discrete scheme. © 1994 John Wiley & Sons, Inc.