Optimal error estimate for a mixed finite element method for compressible Navier--Stokes system

Authors:
Jae Ryong Kweon
Affiliations:
Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, South Korea
Venue:
Applied Numerical Mathematics
Year:
2003

Citing 7
Cited 0

Mixed and hybrid finite element methods

Mixed and hybrid finite element methods
A new mixed finite element for the Stokes and elasticity problems

SIAM Journal on Numerical Analysis
A finite element method for the compressible Stokes equations

SIAM Journal on Numerical Analysis
Compressible Navier-Stokes equations in a bounded domain with inflow boundary condition

SIAM Journal on Mathematical Analysis
A mixed finite element method for a compressible Stokes problem with high Reynolds number

Applied Numerical Mathematics
Finite Element Method for Elliptic Problems

Finite Element Method for Elliptic Problems
A Discontinuous Galerkin Method for Convection-Dominated Compressible Viscous Navier--Stokes Equations with an Inflow Boundary Condition

SIAM Journal on Numerical Analysis

Quantified Score

Hi-index	0.00

Visualization

Abstract

A linearized stationary compressible viscous Navier-Stokes system is considered. A mixed finite element method is applied and the unique existence of the solution is established by the inf-sup condition. The convection terms, especially in the continuity equation, were thought of causing non-optimal order convergence, but in this paper error estimates of optimal order are derived by implementing the lowest order Raviart-Thomas elements. The error estimates for the normal and tangential components of velocity are also optimal on the interfaces of the interior triangles. It turns out that the non-symmetric discrete system can be reformulated into a symmetric form.