Weak Galerkin finite element methods for Parabolic equations

A newly developed weak Galerkin method is proposed to solve parabolic equations. This method allows the usage of totally discontinuous functions in approximation space and preserves the energy conservation law. Both continuous and discontinuous time weak Galerkin finite element schemes are developed...

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Bibliographic Details
Published in:Numerical methods for partial differential equations 2013-11, Vol.29 (6), p.2004-2024
Main Authors: Li, Qiaoluan H., Wang, Junping
Format: Article
Language:English
Subjects:
Approximation
Finite element method
finite element methods
Galerkin methods
Mathematical analysis
Mathematical models
Norms
parabolic equations
Permissible error
Preserves
weak Galerkin methods
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Summary:A newly developed weak Galerkin method is proposed to solve parabolic equations. This method allows the usage of totally discontinuous functions in approximation space and preserves the energy conservation law. Both continuous and discontinuous time weak Galerkin finite element schemes are developed and analyzed. Optimal‐order error estimates in both H1 and L2 norms are established. Numerical tests are performed and reported. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013
ISSN:0749-159X
1098-2426
DOI:10.1002/num.21786