On the structure of the Schur complement matrix for the Stokes equation
Vladislav Pimanov, Ekaterina Muravleva, Ivan Oseledets, Oleg Iliev
TL;DR
This paper analyzes the structure of the Schur complement matrix in discretized Stokes equations, revealing its dependence on eigenvalue characteristics and exploring two key limiting cases.
Contribution
It provides a detailed analysis of how the Schur complement's structure varies with eigenvalue properties in finite-difference discretizations of the Stokes equation.
Findings
Structure depends on the number of non-unit eigenvalues
Two limiting cases are identified and analyzed
Insights could inform better numerical methods for Stokes problems
Abstract
In this paper, we investigate the structure of the Schur complement matrix for the fully-staggered finite-difference discretization of the stationary Stokes equation. Specifically, we demonstrate that the structure of the Schur complement matrix depends qualitatively on a particular characteristic, namely the number of non-unit eigenvalues, and the two limiting cases are of special interest.
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Taxonomy
TopicsMatrix Theory and Algorithms · Nonlinear Dynamics and Pattern Formation · Advanced Differential Equations and Dynamical Systems