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A collocation-Galerkin method for Poisson's equation on rectangular regions

Author: Julio César Díaz
Journal: Math. Comp. 33 (1979), 77-84
MSC: Primary 65N35; Secondary 65N30
MathSciNet review: 514811
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Abstract: A collocation-Galerkin method is defined for Poisson's equation on the unit square, using tensor products of continuous piecewise polynomials. Optimal $ {L^2}$ and $ H_0^1$ orders of convergence are established. This procedure requires fewer quadratures than the corresponding Galerkin procedure.

References [Enhancements On Off] (What's this?)

  • [1] D. ARCHER & J. C. DÍAZ, "A collocation-Galerkin method for a first order hyperbolic equation." (To appear.)
  • [2] JULIO CÉSAR DÍAZ VELASCO, A Hybrid Collocation-Galerkin Method for the Two Point Boundary Value Problem Using Continuous Piecewise Polynomials Spaces, Ph.D. Thesis, Rice Univ., Houston, Texas, 1974.
  • [3] J. C. DÍAZ, "A collocation-Galerkin method for the two point boundary value problem using continuous piecewise polynomial spaces," SIAM J. Numer. Anal., v. 14, 1977, pp. 844-858. MR 0483480 (58:3481)
  • [4] R. J. DUNN & M. F. WHEELER, "Some collocation-Galerkin methods for two-point boundary-value problems," SIAM J. Numer. Anal., v. 13, 1976, pp. 720-733. MR 0433896 (55:6867)
  • [5] P. M. PRENTER & R. D. RUSSELL, "Orthogonal collocation for elliptic partial differential equations," SIAM J. Numer. Anal., v. 13, 1976, pp. 923-939. MR 0426461 (54:14404)
  • [6] M. F. WHEELER, "A $ {C^0}$ collocation-Galerkin method for two-point boundary-value problems and one space dimensional parabolic problems," SIAM J. Numer. Anal., v. 14, 1977, pp. 71-90. MR 0455429 (56:13667)

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Article copyright: © Copyright 1979 American Mathematical Society

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