Finite-element method: accuracy at a point

Author:
Isaac Fried

Journal:
Quart. Appl. Math. **32** (1974), 149-161

MSC:
Primary 65N30

DOI:
https://doi.org/10.1090/qam/436623

MathSciNet review:
436623

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References | Similar Articles | Additional Information

**[1]**G. Strang,*Approximation in the finite element method*, Numer. Math.**19**, 81-98 (1972) MR**0305547****[2]**J. Nitsche,*Ein Kriterium fur die Quasi-Optimalitat des Ritschen Verfahrens*, Numer. Math.**11**, 346-348 (1968) MR**0233502****[3]**J. B. Diaz and H. J. Greenberg,*Upper and lower bounds for the solution of the first boundary value problem of elasticity*, Quart. Appl. Math.**6**, 326-331 (1948) MR**0026529****[4]**J. B. Diaz and H. J. Greenberg,*Upper and lower bounds for the solution of the first biharmonic boundary value problem*, J. Math. Phys.**27**, 193-201 (1948) MR**0026862****[5]**H. Fujita,*Contribution to the theory of upper and lower bounds in boundary value problems*, J. Phys. Soc. Japan**10**, 1-8 (1955) MR**0070256****[6]**C. G. Maple,*The Dirichlet problem: bounds at a point for the solution and its derivatives*, Quart. Appl. Math.**8**, 213-228 (1950) MR**0040499****[7]**K. Washizu,*Bounds for solutions of boundary value problems in elasticity*, J. Math. Phys.**32**, 117-128 (1953) MR**0058415****[8]**J. L. Synge,*The hypercircle in mathematical physics*, Cambridge University Press, 1957 MR**0097605****[9]**L. V. Kantorovich and V. I. Krylov,*Approximate methods of higher analysis*, Interscience Publishers, 1958 MR**0106537****[10]**M. H. Shultz,*Multivariate spline functions and, elliptic problems*, in*Approximations with special emphasis on spline functions*, Academic Press, 1969 MR**0257560****[11]**J. Nitsche,*Linearer Spline-Functionen und die Methoden von Ritz fur elliptische Randwertprobleme*, Arch. Rat. Mech. Anal.**36**, 348-355 (1970) MR**0255043****[12]**S. G. Mikhlin,*Variational methods in mathematical physics*, Pergamon Press, Oxford, 1964 MR**0172493****[13]**M. Zlamal,*On the finite element method*, Numer. Math.**12**, 394-409 (1968) MR**0243753****[14]**M. W. Johnson, Jr. and R. W. McLay,*Convergence of the finite element method in the theory of elasticity*, J. Appl. Mech.**35**, 274-278 (1968)**[15]**E. Hill, G. Szegö and J. D. Tomarkin,*On some generalizations of a theorem by A. Markoff*, Duke Math. J.**3**, 729-739 (1937)**[16]**I. Fried and Shok Keng Yang,*Best finite elements distribution around a singularity*, AIAA J.**10**, 1244-1246 (1972)**[17]**G. Strang,*The finite element method and approximation theory*, in*Numerical solution of partial differential equations*II, ed. B. Hubbard, 1971 MR**0287723****[18]**F. V. Filho, Comment on '*Computation of stress resultants from element stiffness matrices*', AIAA J.**6**, 571-572 (1968)**[19]**B. L. Hulme,*Interpolation by Ritz approximation*, J. Math. Mech.**18**, 337-341 (1968) MR**0231537****[20]**J. H. Bramble and L. E. Payne,*Pointwise bounds in the first biharmonic boundary value problem*, J. Math. Phys.**42**, 278-286 (1963) MR**0159135**

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Additional Information

DOI:
https://doi.org/10.1090/qam/436623

Article copyright:
© Copyright 1974
American Mathematical Society