A FAMILY OF MIMETIC FINITE DIFFERENCE METHODS ON POLYGONAL AND POLYHEDRAL MESHES

2005 ◽  
Vol 15 (10) ◽  
pp. 1533-1551 ◽  
Author(s):  
FRANCO BREZZI ◽  
KONSTANTIN LIPNIKOV ◽  
VALERIA SIMONCINI
Keyword(s):  
Finite Difference ◽  
Material Properties ◽  
Numerical Experiments ◽  
Finite Difference Methods ◽  
Polyhedral Meshes ◽  
Discretization Schemes ◽  
Difference Methods ◽  
Theoretical Results ◽  
Diffusion Problems

A family of inexpensive discretization schemes for diffusion problems on unstructured polygonal and polyhedral meshes is introduced. The material properties are described by a full tensor. The theoretical results are confirmed with numerical experiments.

CONVERGENCE OF MIMETIC FINITE DIFFERENCE METHOD FOR DIFFUSION PROBLEMS ON POLYHEDRAL MESHES WITH CURVED FACES

2006 ◽  
Vol 16 (02) ◽  
pp. 275-297 ◽  
Author(s):  
FRANCO BREZZI ◽  
KONSTANTIN LIPNIKOV ◽  
MIKHAIL SHASHKOV
Keyword(s):  
Finite Difference ◽  
Material Properties ◽  
Variable Pressure ◽  
First Order ◽  
Polyhedral Meshes ◽  
Vector Variable ◽  
Scalar Variable ◽  
Mimetic Finite Difference Method ◽  
Convergence Estimates ◽  
Diffusion Problems

New mimetic finite difference discretizations of diffusion problems on unstructured polyhedral meshes with strongly curved (non-planar) faces are developed. The material properties are described by a full tensor. The optimal convergence estimates, the second order for a scalar variable (pressure) and the first order for a vector variable (velocity), are proved.

scholarly journals On exponential fitting of finite difference methods for heat equations

2021 ◽  
pp. 1-12
Author(s):  
E.O. Tuggen ◽  
C.E. Abhulimen
Keyword(s):  
Stability Analysis ◽  
Finite Difference ◽  
Truncation Error ◽  
Finite Difference Methods ◽  
Exponential Fitting ◽  
Heat Equations ◽  
Local Truncation Error ◽  
Difference Methods ◽  
Exponentially Fitted ◽  
Diffusion Problems

Abstract In this article, a new kind of finite difference scheme that is exponentially fitted, inspired from Fourier analysis, for a fourth space derivative was developed for solving diffusion problems. Dispersion relation and local truncation error of the method were discussed. Stability analysis of the method revealed that it is conditionally stable. Compared to the corresponding fourth order classical scheme in the literature, the proposed scheme is efficient and accurate. Mathematics Subject Classification (2020): 65M06, 65N06. Keywords: Exponential fitting, Finite difference, Local truncation error, Heat equations.

scholarly journals On Modifications of Continuous and Discrete Maximum Principles for Reaction-Diffusion Problems

2011 ◽  
Vol 3 (1) ◽  
pp. 109-120 ◽  
Author(s):  
István Faragó ◽  
Sergey Korotov ◽  
Tamás Szabó
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Finite Difference Methods ◽  
Reaction Diffusion ◽  
Maximum Principles ◽  
Difference Methods ◽  
Sign Conditions ◽  
Diffusion Problems

AbstractIn 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.

scholarly journals Classical and Multisymplectic Schemes for Linearized KdV Equation: Numerical Results and Dispersion Analysis

Fluids ◽  
2021 ◽  
Vol 6 (6) ◽  
pp. 214
Author(s):  
Adebayo Abiodun Aderogba ◽  
Appanah Rao Appadu
Keyword(s):  
Finite Difference ◽  
Numerical Experiments ◽  
Stability Region ◽  
Kdv Equation ◽  
Finite Difference Methods ◽  
Dispersion Analysis ◽  
Explicit Scheme ◽  
Difference Methods ◽  
Relative Errors ◽  
The Stability

We construct three finite difference methods to solve a linearized Korteweg–de-Vries (KdV) equation with advective and dispersive terms and specified initial and boundary conditions. Two numerical experiments are considered; case 1 is when the coefficient of advection is greater than the coefficient of dispersion, while case 2 is when the coefficient of dispersion is greater than the coefficient of advection. The three finite difference methods constructed include classical, multisymplectic and a modified explicit scheme. We obtain the stability region and study the consistency and dispersion properties of the various finite difference methods for the two cases. This is one of the rare papers that analyse dispersive properties of methods for dispersive partial differential equations. The performance of the schemes are gauged over short and long propagation times. Absolute and relative errors are computed at a given time at the spatial nodes used.

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