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Fully discrete interior penalty discontinuous Galerkin methods for nonlinear parabolic equations
Author(s) -
Song Lunji
Publication year - 2012
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.20619
Subject(s) - mathematics , discontinuous galerkin method , sobolev space , nonlinear system , polygon mesh , a priori and a posteriori , norm (philosophy) , galerkin method , mathematical analysis , backward euler method , partial differential equation , parabolic partial differential equation , penalty method , euler equations , finite element method , mathematical optimization , geometry , philosophy , physics , epistemology , quantum mechanics , political science , law , thermodynamics
In this article, we investigate interior penalty discontinuous Galerkin (IPDG) methods for solving a class of two‐dimensional nonlinear parabolic equations. For semi‐discrete IPDG schemes on a quasi‐uniform family of meshes, we obtain a priori bounds on solutions measured in the L 2 norm and in the broken Sobolev norm. The fully discrete IPDG schemes considered are based on the approximation by forward Euler difference in time and broken Sobolev space. Under a restriction related to the mesh size and time step, an h p ‐version of an a priori l ∞ ( L 2 ) and l 2 ( H 1 ) error estimate is derived and numerical experiments are presented.© 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 288–311, 2012
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