A Novel Exponentially Fitted Triangular Finite Element Method for an Advection-Diffusion Problem with Boundary Layers

Journal of Computational Physics

Volumn 134, Issue 2, 1997, Pages 253-260

  Wang, Song ^a  

^a CURTIN UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ADVECTION; BOUNDARY LAYERS; BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; STIFFNESS MATRIX;

ADVECTION-DIFFUSION PROBLEM; EXPONENTIAL BASIS FUNCTIONS; NUMERICAL RESULTS; PERTURBATION PARAMETERS; PIECE-WISE; SINGULAR PERTURBATIONS; SINGULARLY PERTURBED; TRIANGULAR FINITE ELEMENTS; UNSTRUCTURED TRIANGULAR MESHES;

FINITE ELEMENT METHOD;

EID: 0031191437     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1997.5691     Document Type: Article

References (11)

1. Allen D. N. de G., Southwell R. V. Relaxation methods applied to determine the motion, in two dimensions, of a viscous fluid past a fixed cylinder. Quart. J. Mech. Appl. Math. 8:1955;129.
2. Brandt A., Yavneh I. Inadequacy of first-order upwind difference schemes for some circulating flows. J. Comput. Phys. 93:1991;128.
3. Ciarlet P. G. The Finite Element Method for Elliptic Problems. 1978;North-Holland, Amsterdam.
4. Miller J. J. H., Wang S. A new non-conforming Petrov-Galerkin finite element method with triangular elements for a singularity perturbed advection-diffusion problem. IMA J. Numer. Anal. 14:1994;257.
5. Miller J. J. H., Wang S. An exponentially fitted finite element volume method for the numerical solution of 2D unsteady incompressible flow problems. J. Comput. Phys. 115:1994;56.
6. O'Riordan E., Stynes M. A global uniformly convergent finite element method for a singularly perturbed elliptic problem in two dimensions. Math. Comput. 57:1991;47-62.
7. O'Riordan E., Stynes M. An analysis of some exponentially fitted finite element methods for singularly perturbed elliptic problems. Computational Methods for Boundary and Interior Layers in Several Dimensions. 1991;Boole, Dublin. p. 138-.
8. Roos H.-G., Stynes M., Tobiska L. Numerical Methods for Singularly Perturbed Differential Equations. 1996;Springer-Verlag, Berlin/Heidelberg.
9. R. Sacco, E. Gatti, L. Gotusso, 1994, Divergence free shape functions for a finite element solution of the drift-diffusion equations in semiconductors, Dept of Math. Polytechnic of Milan.
10. M. Sever, 1988, Discretization of time-dependent continuity equations, Proceedings of the 6th International NASECODE Conference, J. J. H. Miller, 71, Boole, Dublin.
11. S. Wang, A new exponentially fitted triangular finite element method for the continuity equations in the drift-diffusion model of semiconductor devices.