Weakened acute type condition for tetrahedral triangulations and the discrete maximum principle
نویسندگان
چکیده
We prove that a discrete maximum principle holds for continuous piecewise linear finite element approximations for the Poisson equation with the Dirichlet boundary condition also under a condition of the existence of some obtuse internal angles between faces of terahedra of triangulations of a given space domain. This result represents a weakened form of the acute type condition for the three-dimensional case.
منابع مشابه
On the existence of maximum principles in parabolic finite element equations
In 1973, H. Fujii investigated discrete versions of the maximum principle for the model heat equation using piecewise linear finite elements in space. In particular, he showed that the lumped mass method allows a maximum principle when the simplices of the triangulation are acute, and this is known to generalize in two space dimensions to triangulations of Delauney type. In this note we conside...
متن کاملMesh Adaptation and Discrete Maximum Principle for 2D Anisotropic Diffusion Problems
Finite element method is widely used to solve diffusion problems. For anisotropic problem, the numerical solution may violate the discrete maximum principle (DMP) even if the triangular mesh satisfies acute type condition. We derive the conditions for a triangular mesh such that the obtained solution satisfies DMP. We also develop the strategy to adapt a given mesh so that the solution is impro...
متن کاملError Estimates of a Combined Finite Volume { Finite Element Method for Nonlinear Convection { Diiusion Problems , Mm Aria Lukk a Covv A{medvid'ovv A
The subject of the paper is the analysis of error estimates of the combined nite volume-nite element method for the numerical solution of a scalar nonlinear conservation law equation with a diiusion term. Nonlinear convective terms are approximated with the aid of a monotone nite volume scheme considered over the nite volume mesh dual to a triangular grid, whereas the diiusion term is discretiz...
متن کاملGeneration of Tetrahedral Finite Element Meshes: Variational Delaunay Approach
The goal is to generate tetrahedral decomposition of a general solid body, whose surface is given as a collection of triangular facets. The principle idea is that a vertex set in general positions guarantees existence of a unique triangulation which satisses the Delaunay empty-sphere property. (Algorithms for robust, parallel construction of such triangulations are available.) However, all of t...
متن کاملRobust stability of fuzzy Markov type Cohen-Grossberg neural networks by delay decomposition approach
In this paper, we investigate the delay-dependent robust stability of fuzzy Cohen-Grossberg neural networks with Markovian jumping parameter and mixed time varying delays by delay decomposition method. A new Lyapunov-Krasovskii functional (LKF) is constructed by nonuniformly dividing discrete delay interval into multiple subinterval, and choosing proper functionals with different weighting matr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Math. Comput.
دوره 70 شماره
صفحات -
تاریخ انتشار 2001