A brief note on upwind collocation. (English) Zbl 0513.65068
MSC:
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
Keywords:
upwind collocation; Hermite cubics; orthogonal collocation; non-advective flux; finite element method; diffusion equationReferences:
| [1] | ’An upwind finite element scheme for improved solution of convective-diffusion equation’, Res. Rpt. No. 76-WR-2, Water Resources Program, Princeton University (1976). |
| [2] | Huyakorn, Appl. Math. Modelling 1 pp 187– (1977) |
| [3] | Heinrich, Int. J. Num. Meth. Eng. 11 pp 131– (1977) |
| [4] | Hughes, Int. J. Num. Meth. Eng. 12 pp 1359– (1978) |
| [5] | Pinder, Water Resources Res. 15 pp 1177– (1979) |
| [6] | Shapiro, J. Comp. Phys. 39 pp 46– (1981) |
| [7] | Allen, SPE J. 23 pp 135– (1983) · doi:10.2118/10555-PA |
| [8] | Allen, Int. J. Num. Meth. Eng. (1982) |
| [9] | Gresho, Comp. Fluids 9 pp 223– (1981) |
| [10] | deBoor, SIAM. J. Numer. Anal. 10 pp 582– (1973) |
| [11] | and , Numerical Solution of Partial Differential Equations in Science and Engineering, Wiley-Interscience, New York (1982). · Zbl 0584.65056 |
| [12] | and , Computational Methods in Subsurface Flow, Academic Press, New York (1983). · Zbl 0577.76001 |
| [13] | Payre, Int. J. Num. Meth. Eng. 18 pp 381– (1982) |
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