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Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/10054/11956

Title: An H-1-Galerkin mixed finite element method for parabolic partial differential equations
Authors: PANI, AK
Keywords: order elliptic problems
miscible displacement
convergence analysis
helmholtz-equation
approximation
systems
Issue Date: 1998
Publisher: SIAM PUBLICATIONS
Citation: SIAM JOURNAL ON NUMERICAL ANALYSIS, 35(2), 712-727
Abstract: In this paper, an H-1-Galerkin mixed finite element method is proposed and analyzed for parabolic partial differential equations with nonselfadjoint elliptic parts. Compared to the standard H-1-Galerkin procedure, C-1-continuity for the approximating finite dimensional subspaces can be relaxed for the proposed method. Moreover, it is shown that the finite element approximations have the same rates of convergence as in the classical mixed method, but without LBB consistency condition and quasiuniformity requirement on the finite element mesh. Finally, a better rate of convergence for the flux in L-2-norm is derived using a modified H-1-Galerkin mixed method in two and three space dimensions, which confirms the findings in a single space variable and also improves upon the order of convergence of the classical mixed method under extra regularity assumptions on the exact solution.
URI: http://dx.doi.org/10.1137/S0036142995280808
http://dspace.library.iitb.ac.in/xmlui/handle/10054/11956
http://hdl.handle.net/10054/11956
ISSN: 0036-1429
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