Modified unsymmetric SOR method for saddle-point problems

2014 ◽  
Vol 234 ◽  
pp. 584-598 ◽  
Author(s):  
Zhao-Zheng Liang ◽  
Guo-Feng Zhang
Keyword(s):  
Saddle Point ◽  
Saddle Point Problems ◽  
Sor Method

The corrected Uzawa method for solving saddle point problems

2015 ◽  
Vol 22 (4) ◽  
pp. 717-730 ◽  
Author(s):  
C. F. Ma ◽  
Q. Q. Zheng
Keyword(s):  
Saddle Point ◽  
Uzawa Method ◽  
Saddle Point Problems

General finite-volume framework for saddle-point problems of various physics

2021 ◽  
Vol 36 (6) ◽  
pp. 359-379
Author(s):  
Kirill M. Terekhov
Keyword(s):  
Saddle Point ◽  
Finite Volume ◽  
Navier Stokes ◽  
Saddle Point Problems ◽  
Surface Integral ◽  
Matrix Coefficients ◽  
Gauss Theorem ◽  
Stability Issue ◽  
Incompressible Elasticity ◽  
Vector Flux

Abstract This article is dedicated to the general finite-volume framework used to discretize and solve saddle-point problems of various physics. The framework applies the Ostrogradsky–Gauss theorem to transform a divergent part of the partial differential equation into a surface integral, approximated by the summation of vector fluxes over interfaces. The interface vector fluxes are reconstructed using the harmonic averaging point concept resulting in the unique vector flux even in a heterogeneous anisotropic medium. The vector flux is modified with the consideration of eigenvalues in matrix coefficients at vector unknowns to address both the hyperbolic and saddle-point problems, causing nonphysical oscillations and an inf-sup stability issue. We apply the framework to several problems of various physics, namely incompressible elasticity problem, incompressible Navier–Stokes, Brinkman–Hazen–Dupuit–Darcy, Biot, and Maxwell equations and explain several nuances of the application. Finally, we test the framework on simple analytical solutions.

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