Analysis of a projection/characteristic scheme for incompressible flow

Communications in Numerical Methods in Engineering

Volumn 19, Issue 7, 2003, Pages 535-550

  Guermond, Jean Luc ^a   Minev, Peter D ^b  

^a CNRS   (France)

^b UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Finite element method; Method of characteristics; Projection methods

Indexed keywords

COSTS; NAVIER STOKES EQUATIONS; VELOCITY MEASUREMENT;

ADVECTION;

INCOMPRESSIBLE FLOW;

FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; MATHEMATICAL ANALYSIS; NAVIER-STOKES EQUATIONS;

EID: 0041972492     PISSN: 10698299     EISSN: None     Source Type: Journal    
DOI: 10.1002/cnm.611     Document Type: Article

References (12)

1. Achdou Y, Guermond J-L. Convergence analysis of a finite element projection/Lagrange-Galerkin method for the incompressible Navier-Stokes equations. SIAM Journal on Numerical Analysis 2000; 37(3):799-826.
2. Minev PD, Ethier CR. A semi-implicit projection algorithm for the Navier-Stokes equations with application to flows in complex geometries. In Notes on Numerical Fluid Mechanics, vol. 73, Griebel et al. (eds). Vieweg: Braunschweig/Wiesbaden, 1999; 223-231.
3. Guermond J-L, Quartapelle L. On the approximation of the unsteady Navier-Stokes equations by finite element projection methods. Numerische Mathematik 1998; 80:207-238.
4. Pironneau O. On the transport-diffusion algorithm and its applications to the Navier-Stokes equations. Numerische Mathematik 1982; 38:309-332.
5. Boukir K, Maday Y, Metivet B, Razafindrakoto E. A high order characteristics/finite element method for the incompressible Navier-Stokes equations. International Journal for Numerical Methods in Fluids 1997; 25:1421-1454.
6. Douglas J, Russell TF. Numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element methods or finite difference method. SIAM Journal on Numerical Analysis 1982; 19:871-885.
7. Stepleman RS (eds), Advances in Computational Methods for P.D.E. 1981; 28-36.
8. Süli E. Convergence and non-linear stability of the Lagrange-Galerkin method for the Navier-Stokes equations. Numerische Mathematik 1988; 53:459-483.
9. Gresho PM, Chan ST. On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. Part I and Part II. International Journal for Numerical Methods in Fluids 1990; 11:587-620.
10. Ciarlet PG. The Finite Element Method for Elliptic Problems. North-Holland: Amsterdam, 1978.
11. Morton KW, Priestley A, Sǔli E. Stability of the Lagrange-Galerkin method with non-exact integration. Mathematical Modelling in Numerical Analysis 1988; 22:625-653.
12. Ethier CR, Steinman DA. Exact fully 3-D Navier-Stokes solution for benchmarking. International Journal for Numerical Methods in Fluids 1994; 19:369-375.