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Global well‐posedness of classical solutions with large oscillations and vacuum to the three‐dimensional isentropic compressible Navier‐Stokes equations
We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the isentropic compressible Navier‐Stokes equations in three spatial dimensions with smooth initial…
FETI‐DP, BDDC, and block Cholesky methods
With the new formulation of these algorithms, a simplified proof is provided that the spectra of a pair of FETI‐DP and BDDC algorithms, with the same set of primal constraints, are essentially the same.
Asymptotic Stability of Combination of Viscous Contact Wave with Rarefaction Waves for One-Dimensional Compressible Navier–Stokes System
We are concerned with the large-time behavior of solutions of the Cauchy problem to the one-dimensional compressible Navier–Stokes system for ideal polytropic fluids, where the far field states are…
Vanishing of Vacuum States and Blow-up Phenomena of the Compressible Navier-Stokes Equations
The Navier-Stokes systems for compressible fluids with density-dependent viscosities are considered in the present paper. These equations, in particular, include the ones which are rigorously derived…
Global Well-Posedness and Large Time Asymptotic Behavior of Classical Solutions to the Compressible Navier–Stokes Equations with Vacuum
We are concerned with the global well-posedness and large time asymptotic behavior of strong and classical solutions to the Cauchy problem of the Navier–Stokes equations for viscous compressible…
Global Existence of Weak Solutions to the Barotropic Compressible Navier-Stokes Flows with Degenerate Viscosities
This paper concerns the existence of global weak solutions to the barotropic compressible Navier-Stokes equations with degenerate viscosity coefficients. We construct suitable approximate system…
FETI-DPH: A DUAL-PRIMAL DOMAIN DECOMPOSITION METHOD FOR ACOUSTIC SCATTERING
A dual-primal variant of the FETI-H domain decomposition method is designed for the fast, parallel, iterative solution of large-scale systems of complex equations arising from the discretization of…
BDDC Algorithms for Incompressible Stokes Equations
The purpose of this paper is to extend the balancing domain decomposition by constraints (BDDC) algorithm to saddle‐point problems that arise when mixed finite element methods are used to approximate…
On the use of inexact subdomain solvers for BDDC algorithms
A Dual-Primal FETI method for incompressible Stokes equations
- Jing Li
- Computer Science, MathematicsNumerische Mathematik
- 1 December 2005
A dual-primal FETI method is developed for incompressible Stokes equations approximated by mixed finite elements with discontinuous pressures and it is proved that the condition number of this preconditioned dual problem is independent of the number of subdomains and bounded from above.