Mixed finite volume methods

International Journal for Numerical Methods in Engineering

Volumn 46, Issue 9, 1999, Pages 1351-1366

  Thomas, J M ^a   Trujillo, D ^b  

^a UNIVERSITÉ DE PAU ET DES PAYS DE L'ADOUR   (France)

^b NONE

Author keywords

A priori error estimates; Finite volume; Generalized inf sup conditions; Mixed finite element; Second order elliptic problem; Vertex centered scheme

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; DIFFUSION; ERROR ANALYSIS; FINITE ELEMENT METHOD;

MIXED FINITE VOLUME METHOD; NEUMANN BOUNDARY CONDITION;

FINITE VOLUME METHOD;

EID: 0039772290     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19991130)46:9<1351::AID-NME702>3.0.CO;2-0     Document Type: Article

References (13)

1. Cai Z. On the finite volume element method. Numerical Mathematics 1991; 58:713-735.
2. Cai Z, Mandel J, McCormick S. The finite volume element method for diffusion equations on general triangulations. SIAM Journal of Numerical Analysis 1991; 28:392-402.
3. Thomas J-M, Trujillo D. Finite volume variational formulation. Application to domain decomposition methods. In Domain Decomposition Methods in Sciences and Engineering, Sixth International Conference on Domain Decomposition Methods in Science and Engineering, Quarteroni A et al. (eds). AMS Series, Contemporary Mathematics, 1994; 157:127-132.
4. Thomas J-M, Trujillo D. Analysis of finite volume methods and application to reservoir simulation. In Proceedings of the Conference: Mathematical Modelling of Flow through Porous Media, Bourgeat A, Carasso C, Luckhaus S, Mikelic A (eds). World Scientific: Singapore, 1995; 318-336.
5. Thomas J-M, Trujillo D. Finite volume methods for elliptic problems; Convergence on unstructured meshes. In Numerical Methods in Mechanics, Conca C, Gatica G (eds). Pitman Research Notes in Mathematics Series, vol. 371. Addison-Wesley Longman: Reading MA, 1997; 163-174.
6. Cai Z, Jones J, McCormick S, Russell T. Control-volume mixed finite element methods. Computational Geosciences, 1997; 1:289-315.
7. Eymard R, Gallouët T, Herbin R. The finite volume method. In Handbook of Numerical Analysis, vol. VII. Ciarlet PG, Lions JL (eds). Elsevier Science: Amsterdam, to appear.
8. Trujillo D. Couplage espace-temps de schémas numériques en simulation de réservoir. Thèse, Université de Pau et des Pays de l'Adour, 1994.
9. Nicolaïdes RA. Existence, uniqueness and approximation for generalized saddle-point problems. SIAM Journal of Numerical Analysis 1982; 19:349-357.
10. Bernardi C, Canuto C, Maday Y. Generalized inf-sup conditions for Chebychev spectral approximation of Stokes problem, SIAM Journal of Numerical Analysis 1988; 25:1237-1271.
11. Ciarlet PG. Basic error estimates for elliptic problems. In Handbook of Numerical Analysis, Finite Element Methods, vol. II, Finite Element Methods (Part 1). Ciarlet PG, Lions JL (eds). North-Holland: Amsterdam, 1991; 17-351.
12. Raviart P-A, Thomas J-M. A Mixed Finite Element Method for Second Order Elliptic Problems. In Mathematical Aspects of the Finite Element Method, Lecture Notes in Mathematics, vol. 606. Springer: Berlin, 1977; 292-315.
13. Roberts JE, Thomas J-M. Mixed and hybrid methods. In Handbook of Numerical Analysis, Finite Element Methods, vol. II, Finite Element Methods (Part 1). Ciarlet PG, Lions JL (eds). North-Holland: Amsterdam, 1991; 523-639.