Discrete maximum principle for parabolic problems solved by prismatic finite elements
نویسندگان
چکیده
In this paper we analyze the discrete maximum principle (DMP) for a nonstationary diffusion-reaction problem solved by means of prismatic finite elements and θmethod. We derive geometric conditions on the shape parameters of prismatic partitions and time-steps which guarantee validity of the DMP. The presented numerical tests illustrate the sharpness of the obtained conditions. MSC: 65M60, 65M20, 35B50, 35K20
منابع مشابه
Discrete maximum principle for 3D-FE solutions of the diffusion-reaction problem on prismatic meshes
In this paper we analyse the discrete maximum principle (DMP) for a stationary diffusion-reaction problem solved by means of prismatic finite elements. We derive geometric conditions on the shape parameters of the prismatic partitions which guarantee validity of the DMP. The presented numerical tests show the sharpness of the obtained conditions.
متن کاملOn a Discrete Maximum Principle for Linear FE Solutions of Elliptic Problems with a Nondiagonal Coefficient Matrix
In this paper we present a sufficient condition for the validity of a discrete maximum principle (DMP) for a class of elliptic problems of the second order with a nondiagonal coefficient matrix, solved by means of linear finite elements (FEs). Numerical tests are presented.
متن کاملVARIATIONAL DISCRETIZATION AND MIXED METHODS FOR SEMILINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS WITH INTEGRAL CONSTRAINT
The aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Optimal error estimates in L2 are established for the state...
متن کاملDiscrete 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 کاملContinuous and discrete parabolic operators and their qualitative properties
The basic requirement of numerical methods is convergence. However, from the practical point of view, it is generally not sufficient to construct convergent numerical methods for the solutions of partial differential equations. The qualitative adequateness of the methods is also an issue. The numerical solutions should mirror the characteristic properties of the original physical process that i...
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:
- Mathematics and Computers in Simulation
دوره 80 شماره
صفحات -
تاریخ انتشار 2010