Interior Penalty Discontinuous Galerkin Methods with Implicit Time-Integration Techniques for Nonlinear Parabolic Equations

Content Provider	Semantic Scholar
Author	Song, Lunji Gie, Gung-Min Shiue, Ming-Cheng
Copyright Year	2012
Abstract	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 l2(H 1) and l∞(L2) 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 29: 1341–1366, 2013
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://www.math.louisville.edu/~gie/SGS_12.pdf
Alternate Webpage(s)	http://math.ucr.edu/~ggie/SGS_12.pdf
Alternate Webpage(s)	https://ir.nctu.edu.tw/bitstream/11536/21629/1/000318177700012.pdf
Language	English
Access Restriction	Open
Subject Keyword	Approximation Crank (person) Crank–Nicolson method DNA Integration Discontinuous Galerkin method Estimated Euler Experiment Finite difference Lipomatosis, Multiple Symmetrical Methamphetamine Navier–Stokes equations Nonlinear system Numerical analysis Numerical stability Parabolic antenna Solutions
Content Type	Text
Resource Type	Article