Convergence analysis for an exponentially fitted finite volume method
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 34 (2000) no. 6, p. 1165-1188
@article{M2AN_2000__34_6_1165_0,
     author = {Vanselow, Reiner},
     title = {Convergence analysis for an exponentially fitted finite volume method},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {34},
     number = {6},
     year = {2000},
     pages = {1165-1188},
     zbl = {0974.65098},
     mrnumber = {1812732},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2000__34_6_1165_0}
}
Vanselow, Reiner. Convergence analysis for an exponentially fitted finite volume method. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 34 (2000) no. 6, pp. 1165-1188. http://www.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 1323737 | Zbl 0831.65117

[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 1069278 | Zbl 0713.65066

[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 0912.68084

[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 1399499 | Zbl 0857.65116

[5] D. Braess, Finite Elemente. Springer, Berlin (1992). | Zbl 0754.65084

[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 1115237 | Zbl 0875.65086

[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 1681308 | Zbl 0930.65118

[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 1635463 | Zbl 0915.65128

[9] B. Heinrich, Finite Difference Methods on Irregular Networks. A Generalized Approach to Second Order Problems. Akademie, Berlin (1987). | MR 875416 | Zbl 0606.65065

[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 1316144 | Zbl 0822.65085

[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 1268995 | Zbl 0806.65111

[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 1445295 | Zbl 0861.65070

[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 1432132 | Zbl 0885.65121

[16] H.G. Roos, M. Stynes and L. Tobiska, Numerical Methods for Singularly Perturbed Differential Equations. Springer, London(1996). | MR 1477665 | Zbl 0844.65075

[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 1605547 | Zbl 0907.65110

[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 1674361 | Zbl 0926.65119

[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 2062137 | Zbl 1052.65558

[20] L.L. Schumaker, Spline Functions: Basic Theory. Wiley, New York (1981). | MR 606200 | Zbl 0449.41004

[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 413554 | Zbl 0264.65068

[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 1605414 | Zbl 0903.65084

[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 1654022 | Zbl 0931.65111