Convergence analysis for an exponentially fitted finite volume method
ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 6, pp. 1165-1188. 
@article{M2AN_2000__34_6_1165_0,
     author = {Vanselow, Reiner},
     title = {Convergence analysis for an exponentially fitted finite volume method},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {1165--1188},
     publisher = {Dunod},
     address = {Paris},
     volume = {34},
     number = {6},
     year = {2000},
     mrnumber = {1812732},
     zbl = {0974.65098},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_2000__34_6_1165_0/}
}
TY  - JOUR
AU  - Vanselow, Reiner
TI  - Convergence analysis for an exponentially fitted finite volume method
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 2000
SP  - 1165
EP  - 1188
VL  - 34
IS  - 6
PB  - Dunod
PP  - Paris
UR  - http://archive.numdam.org/item/M2AN_2000__34_6_1165_0/
LA  - en
ID  - M2AN_2000__34_6_1165_0
ER  - 
%0 Journal Article
%A Vanselow, Reiner
%T Convergence analysis for an exponentially fitted finite volume method
%J ESAIM: Modélisation mathématique et analyse numérique
%D 2000
%P 1165-1188
%V 34
%N 6
%I Dunod
%C Paris
%U http://archive.numdam.org/item/M2AN_2000__34_6_1165_0/
%G en
%F M2AN_2000__34_6_1165_0
Vanselow, Reiner. Convergence analysis for an exponentially fitted finite volume method. ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 6, pp. 1165-1188. http://archive.numdam.org/item/M2AN_2000__34_6_1165_0/

[1] L. Angermann, Error Estimate for the Finite-Element Solution of an Elliptic Singularly Perturbed Problem. IMA J. Numer. Anal 15 (1995) 161-196. | MR | Zbl

[2] R.E. Bank, J.F. Bürgler, W. Fichtner and R.K. Smith, Some Upwinding Techniques for Finite Element Approximations of Convection-Diffusion Equations. Numer. Math. 58 (1990) 185-202. | MR | Zbl

[3] R.E. Bank, W.M. Jr. Coughran and L.C. Cowsar, The Finite Volume Scharfetter-Gummel Method for Steady Convection Diffusion Equations. Comput. Visual Sci. 1 (1998) 123-136. | Zbl

[4] J. Baranger, J.-F. Maître and F. Oudin, Connection between Finite Volume and Mixed Finite Element Methods. RAIRO Modél. Math. Anal. Numér. 30 (1996) 445-465. | Numdam | MR | Zbl

[5] D. Braess, Finite Elemente. Springer, Berlin (1992). | Zbl

[6] P.G. Ciarlet, Basic Error Estimates for Elliptic Problems, in Handbook of Numerical Analysis, Vol. II, Part 1, P.G. Ciarlet and J.L. Lions Eds., Elsevier, Amsterdam (1991) 17-351. | MR | Zbl

[7] R. Eymard, T. Gallouet and R. Herbin, Convergence of Finite Volume Schemes for Semilinear Convection Diffusion Equations. Numer. Math. 1 (1999) 1-26. | MR | Zbl

[8] E. Gatti, S. Micheletti and R. Sacco, A New Galerkin Framework for the Drift-Diffusion Equation in Semiconductors. East-West J. Numer. Math. 6 (1998) 101-135. | MR | Zbl

[9] B. Heinrich, Finite Difference Methods on Irregular Networks. A Generalized Approach to Second Order Problems. Akademie, Berlin (1987). | MR | Zbl

[10] R. Herbin, An Error Estimate for a Finite Volume Scheme for a Diffusion-Convection Problem on a Triangular Mesh. Numer. Methods Partial Differential Equations 11 (1995) 165-173. | MR | Zbl

[11] R.D. Lazarov and I.D. Mishev, Finite Volume Methods for Reaction-Diffusion Problems, in Finite Volumes for Complex Applications, F. Benkhaldoun and R. Vilsmeier Eds., Hermes, Paris (1996) 231-240.

[12] J.J.H. Miller and S. Wang, A New Non-Conforming Petrov-Galerkin Finite Element Method with Triangular Elements for an Advection-Diffusion Problem. IMA J. Numer. Anal. 14 (1994) 257-276. | MR | Zbl

[13] I.D. Mishev, Finite Volume and Finite Volume Element Methods for Nonsymmetric Problems. Ph.D. thesis, Texas A&M University (1996).

[14] K.W. Morton, Numerical Solution of Convection-Diffusion Problems. Chapman and Hall, London (1996). | MR | Zbl

[15] K.W. Morton, M. Stynes and E. Süli, Analysis of a Cell-Vertex Finite Volume Method for Convection-Diffusion Problems, Math. Comp. 66 (1997) 1369-1406. | MR | Zbl

[16] H.G. Roos, M. Stynes and L. Tobiska, Numerical Methods for Singularly Perturbed Differential Equations. Springer, London(1996). | MR | Zbl

[17] R. Sacco and M. Stynes, Finite Element Methods for Convection-Diffusion Problems Using Exponential Splines on Triangles. Comput. Math. Appl 35 (1998) 35-45. | MR | Zbl

[18] R. Sacco, E. Gatti and L. Gotusso, A Nonconforming Exponentially Fitted Finite Element Method for Two-Dimensional Drift-Diffusion Models in Semiconductors. Numer. Methods Partial Differential Equations 15 (1999) 133-150. | MR | Zbl

[19] H.-P. Scheffler and R. Vanselow, Convergence Analysis of a Cell-Centered FVM, in Finite Volumes for Complex Applications II, R. Vilsmeier, F. Benkhaldoun and D. Hänel Eds., Hermes, Paris (1999) 181-188. | MR | Zbl

[20] L.L. Schumaker, Spline Functions: Basic Theory. Wiley, New York (1981). | MR | Zbl

[21] S. Selberherr, Analysis and Simulation of Semiconductor Devices. Springer, Wien (1984).

[22] G. Strang, Variational Crimes in the Finite Element Method, in The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, A.K. Aziz Ed., Academic Press (1972) 689-710. | MR | Zbl

[23] R. Vanselow and H.-P. Scheffler, Convergence Analysis of a Finite Volume Method via a New Nonconforming Finite Element Method. Numer. Methods Partial Differential Equations 14 (1998) 213-231. | MR | Zbl

[24] R. Vanselow, Convergence Analysis for an Exponentially Fitted FVM. Preprint MATH-NM-09-99, TU Dresden (1999).

[25] J. Xu and L. Zikatanov, A Monotone Finite Element Scheme for Convection-Diffusion Equations. Math. Comp. 68 (1999) 1429-1446. | MR | Zbl