On Weakening Conditions for Discrete Maximum Principles for Linear Finite Element Schemes
نویسندگان
چکیده
In this work we discuss weakening requirements on the set of sufficient conditions due to Ph. Ciarlet [4, 5] for matrices associated to linear finite element schemes, which is commonly used for proving validity of discrete maximum principles (DMPs) for the second order elliptic problems. AMS subject classifications: 65N30, 65N50
منابع مشابه
Discrete maximum principles for nonlinear parabolic
Discrete maximum principles are established for finite element approximations 10 of nonlinear parabolic PDE systems with mixed boundary and interface conditions. The 11 results are based on an algebraic discrete maximum principle for suitable ODE systems. 12
متن کاملGradient-based nodal limiters for artificial diffusion operators in finite element schemes for transport equations
This paper presents new linearity-preserving nodal limiters for enforcing discrete maximum principles in continuous (linear or bilinear) finite element approximations to transport problems with steep fronts. In the process of algebraic flux correction, the oscillatory antidiffusive part of a high-order base discretization is decomposed into a set of internodal fluxes and constrained to be local...
متن کاملPropagation of Crack in Linear Elastic Materials with Considering Crack Path Correction Factor
Modeling of crack propagation by a finite element method under mixed mode conditions is of prime importance in the fracture mechanics. This article describes an application of finite element method to the analysis of mixed mode crack growth in linear elastic fracture mechanics. Crack - growth process is simulated by an incremental crack-extension analysis based on the maximum principal stress c...
متن کاملOn Nonobtuse Refinements of Tetrahedral Finite Element Meshes
It is known that piecewise linear continuous finite element (FE) approximations on nonobtuse tetrahedral FE meshes guarantee the validity of discrete analogues of various maximum principles for a wide class of elliptic problems of the second order. Such analogues are often called discrete maximum principles (or DMPs in short). In this work we present several global and local refinement techniqu...
متن کاملOnModifications of Continuous and Discrete Maximum Principles for Reaction-Diffusion Problems
In this work, we present and discuss some modifications, in the form of two-sided estimation (and also for arbitrary source functions instead of usual sign-conditions), of continuous and discrete maximum principles for the reactiondiffusion problems solved by the finite element and finite difference methods. AMS subject classifications: 35B50, 65N06, 65N30, 65N50
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008