scholarly journals MODIFIED FINITE-DIFFERENCE SCHEME FOR SOLVING ONE CLASS OF CONVECTION-REACTION-DIFFUSION PROBLEMS

2021 ◽  
pp. 7-14
Author(s):  
Anna Vladimirovna Pavelchuk ◽  
◽  
Anna Gennadievna Maslovskaya ◽  
Keyword(s):  
Finite Difference ◽  
Finite Difference Methods ◽  
Reaction Diffusion ◽  
Time Dependent ◽  
Computational Scheme ◽  
Multidimensional Equation ◽  
Difference Methods ◽  
Alternating Directions Method ◽  
Diffusion Convection ◽  
Diffusion Problems

The paper reviews approaches to the construction of finite-difference methods for solving time-dependent diffusion equations and transport equations. A modified computational scheme for solving a semilinear multidimensional equation of the «reaction – diffusion – convection» type is presented. The hybrid computational scheme is based on the alternating directions method and the Robert-Weiss scheme.

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.

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.

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