Effective difference schemes for parabolic systems of equations

1964 ◽  
Vol 4 (5) ◽  
pp. 193-198
Author(s):  
A.A. Samarskii
Keyword(s):  
Parabolic Systems ◽  
Difference Schemes ◽  
Systems Of Equations

scholarly journals Monotone Difference Schemes for Weakly Coupled Elliptic and Parabolic Systems

2017 ◽  
Vol 17 (2) ◽  
pp. 287-298 ◽  
Author(s):  
Piotr Matus ◽  
Francisco Gaspar ◽  
Le Minh Hieu ◽  
Vo Thi Kim Tuyen
Keyword(s):  
A Priori Estimate ◽  
Parabolic Systems ◽  
Uniform Norm ◽  
Difference Schemes ◽  
Scalar Case ◽  
Quasilinear Parabolic Equations ◽  
Positivity Condition ◽  
Weakly Coupled ◽  
Weakly Coupled System ◽  
Vector Difference

AbstractThe present paper is devoted to the development of the theory of monotone difference schemes, approximating the so-called weakly coupled system of linear elliptic and quasilinear parabolic equations. Similarly to the scalar case, the canonical form of the vector-difference schemes is introduced and the definition of its monotonicity is given. This definition is closely associated with the property of non-negativity of the solution. Under the fulfillment of the positivity condition of the coefficients, two-side estimates of the approximate solution of these vector-difference equations are established and the important a priori estimate in the uniform normCis given.

FINITE DIFFERENCE SCHEMES WITH CROSS DERIVATIVES CORRECTORS FOR MULTIDIMENSIONAL PARABOLIC SYSTEMS

2006 ◽  
Vol 03 (01) ◽  
pp. 27-52 ◽  
Author(s):  
FRANÇOIS BOUCHUT ◽  
HERMANO FRID
Keyword(s):  
Finite Difference ◽  
Parabolic Systems ◽  
Finite Volume Methods ◽  
Difference Schemes ◽  
Navier Stokes ◽  
Finite Difference Schemes ◽  
First Order ◽  
Flux Vector Splitting ◽  
Cross Derivatives ◽  
Mixed Derivatives

We propose finite difference schemes for multidimensional quasilinear parabolic systems whose main feature is the introduction of correctors which control the second-order terms with mixed derivatives. We show that with these correctors the schemes inherit physically relevant properties present at the continuous level, such as the existence of invariant domains and/or the nonincrease of the total amount of entropy. The analysis is performed with some general tools that could be used also in the analysis of finite volume methods based on flux vector splitting for first-order hyperbolic problems on unstructured meshes. Applications to the compressible Navier–Stokes system are given.

scholarly journals On some classes of coefficient inverse problems for parabolic systems of equations with the ovedetermination date of evolutionary type

2015 ◽  
Vol 11 (3) ◽  
pp. 51-57
Author(s):  
Ekaterina M Korotkova
Keyword(s):  
Inverse Problems ◽  
Parabolic System ◽  
Local Existence ◽  
Parabolic Systems ◽  
System Of Equations ◽  
Systems Of Equations ◽  
Local Existence Theorem ◽  
Coefficient Inverse Problems ◽  
Boundary Operators ◽  
Parabolic System Of Equations

The article is devoted to the question of wellposedness in the Sobolev spaces of inverse problems on determining the righthand side and coefficients in a parabolic system of equations. The overdetermination conditions are the values of a part of the vector of solutions on some system of surfaces. Under special conditions on the boundary operators the local existence theorem of solutions to the problem is established.

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