Galerkin/Runge-Kutta discretizations of nonlinear parabolic equations

Summary, in English

Global error bounds are derived for full Galerkin/Runge-Kutta discretizations of nonlinear parabolic problems, including the evolution governed by the p-Laplacian with p >= 2. The analysis presented here is not based on linearization procedures, but on the fully nonlinear framework of logarithmic Lipschitz constants and an extended B-convergence theory. The global error is bounded in L-2 by Delta x(r/2) + Delta t(q). where r is the convergence order of the Galerkin method applied to the underlying stationary problem and q is the stiff order of the algebraically stable Runge-Kutta method. (c) 2006 Elsevier B.V. All rights reserved.

• Författare: Eskil Hansen
• Avdelning/ar: Matematik LTH; Partial differential equations; Numerical Analysis
• Publiceringsår: 2007
• Språk: Engelska
• Sidor: 882-890
• Publikation/Tidskrift/Serie: Journal of Computational and Applied Mathematics
• Volym: 205
• Issue: 2
• Länkar: http://dx.doi.org/10.1016/j.cam.2006.03.041
• Dokumenttyp: Artikel i tidskrift
• Förlag: Elsevier
• Ämne: Mathematics
• Nyckelord: logarithmic Lipschitz constants; nonlinear parabolic equations; Galerkin/Runge-Kutta methods; B-convergence
• Status: Published
• Forskningsgrupp: Partial differential equations; Numerical Analysis
• ISBN/ISSN/Övrigt: ISSN: 0377-0427