A least squares decomposition method for solving elliptic equations

Author:
Dennis C. Jespersen

Journal:
Math. Comp. **31** (1977), 873-880

MSC:
Primary 65N30

MathSciNet review:
0461948

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper analyzes a numerical method for solving second-order elliptic partial differential equations. The idea is to write the equation as a lower-order system and solve the system using least squares techniques. Error estimates are derived for a model problem.

**[1]**Ivo Babuška and A. K. Aziz,*Survey lectures on the mathematical foundations of the finite element method*, The mathematical foundations of the finite element method with applications to partial differential equations (Proc. Sympos., Univ. Maryland, Baltimore, Md., 1972) Academic Press, New York, 1972, pp. 1–359. With the collaboration of G. Fix and R. B. Kellogg. MR**0421106****[2]**James H. Bramble and Joachim A. Nitsche,*A generalized Ritz-least-squares method for Dirichlet problems*, SIAM J. Numer. Anal.**10**(1973), 81–93. MR**0314284****[3]**J. H. Bramble and A. H. Schatz,*Least squares methods for 2𝑚th order elliptic boundary-value problems*, Math. Comp.**25**(1971), 1–32. MR**0295591**, 10.1090/S0025-5718-1971-0295591-8**[4]**James H. Bramble and Vidar Thomée,*Semidiscrete least-squares methods for a parabolic boundary value problem*, Math. Comp.**26**(1972), 633–648. MR**0349038**, 10.1090/S0025-5718-1972-0349038-4**[5]**D. JESPERSEN,*A Least Squares Decomposition Method for the Numerical Solution of Elliptic Partial Differential Equations*, Dissertation, University of Michigan, 1976.**[6]**J.-L. Lions and E. Magenes,*Problèmes aux limites non homogènes et applications. Vol. 1*, Travaux et Recherches Mathématiques, No. 17, Dunod, Paris, 1968 (French). MR**0247243****[7]**Paul P. Lynn and Santosh K. Arya,*Use of the least squares criterion in the finite element formulation*, Internat. J. Numer. Methods Engrg.**6**(1973), 75–88. MR**0329410****[8]**J. Nitsche,*Ein Kriterium für die Quasi-Optimalität des Ritzschen Verfahrens*, Numer. Math.**11**(1968), 346–348 (German). MR**0233502****[9]**J. N. Reddy and J. T. Oden,*Mixed finite-element approximations of linear boundary-value problems*, Quart. Appl. Math.**33**(1975/76), no. 3, 255–280. MR**0451782****[10]**R. TEMAM,*On the Theory and Numerical Analysis of the Navier-Stokes Equations*, Lecture Notes, University of Maryland, 1973.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1977-0461948-0

Keywords:
Rayleigh-Ritz Galerkin methods,
least squares approximation,
mixed methods

Article copyright:
© Copyright 1977
American Mathematical Society