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

DOI:
https://doi.org/10.1090/S0025-5718-1979-0514811-2

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 and orders of convergence are established. This procedure requires fewer quadratures than the corresponding Galerkin procedure.

**[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 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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DOI:
https://doi.org/10.1090/S0025-5718-1979-0514811-2

Article copyright:
© Copyright 1979
American Mathematical Society