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Interior penalty discontinuous Galerkin methods with implicit time‐integration techniques for nonlinear parabolic equations
Author(s) -
Song Lunji,
Gie GungMin,
Shiue MingCheng
Publication year - 2013
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.21758
Subject(s) - mathematics , discontinuous galerkin method , backward euler method , nonlinear system , stability (learning theory) , galerkin method , partial differential equation , penalty method , mathematical analysis , parabolic partial differential equation , partial derivative , euler equations , finite element method , mathematical optimization , computer science , physics , quantum mechanics , machine learning , thermodynamics
We prove existence and numerical stability of numerical solutions of three fully discrete interior penalty discontinuous Galerkin methods for solving nonlinear parabolic equations. Under some appropriate regularity conditions, we give the l 2 ( H 1 ) and l ∞ ( L 2 ) error estimates of the fully discrete symmetric interior penalty discontinuous Galerkin–scheme with the implicit θ ‐schemes in time, which include backward Euler and Crank–Nicolson finite difference approximations. Our estimates are optimal with respect to the mesh size h . The theoretical results are confirmed by some numerical experiments. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013