کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4602905 1336942 2008 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The discrete maximum principle for linear simplicial finite element approximations of a reaction–diffusion problem
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
The discrete maximum principle for linear simplicial finite element approximations of a reaction–diffusion problem
چکیده انگلیسی

This paper provides a sufficient condition for the discrete maximum principle for a fully discrete linear simplicial finite element discretization of a reaction–diffusion problem to hold. It explicitly bounds the dihedral angles and heights of simplices in the finite element partition in terms of the magnitude of the reaction coefficient and the spatial dimension. As a result, it can be computed how small the acute simplices should be for the discrete maximum principle to be valid. Numerical experiments suggest that the bound, which considerably improves a similar bound in [P.G. Ciarlet, P.-A. Raviart, Maximum principle and uniform convergence for the finite element method, Comput. Methods Appl. Mech. Eng. 2 (1973) 17–31.], is in fact sharp.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 429, Issue 10, 1 November 2008, Pages 2344-2357