Maximum norm contractivity of discretization schemes for the heat equation
Applied Numerical Mathematics
Maximum norm contractivity in the numerical solution of the one-dimensional heat equation
Applied Numerical Mathematics
Weakened acute type condition for tetrahedral triangulations and the discrete maximum principle
Mathematics of Computation
On Monotonicity of Difference Schemes for Computational Physics
SIAM Journal on Scientific Computing
Discrete maximum principle for linear parabolic problems solved on hybrid meshes
Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Discrete Maximum Principle and Adequate Discretizations of Linear Parabolic Problems
SIAM Journal on Scientific Computing
Numerical Analysis and Its Applications
| Hi-index | 0.09 |
New numerical models for simulation of physical and chemical phenomena have to meet certain qualitative requirements, such as nonnegativity preservation, maximum-minimum principle, and maximum norm contractivity. For parabolic initial boundary value problems, these properties are generally guaranteed by certain geometrical conditions on the meshes used and by choosing the time-step according to some lower and upper bounds. The necessary and sufficient conditions of the qualitative properties and their relations have been already given. In this paper sufficient conditions are derived for the Galerkin finite element solution of a linear parabolic initial boundary value problem. We solve the problem on a 2D rectangular domain using bilinear basis function.