Abstract
The purpose of this paper is to measure, with explicit constants as small as possible, a priori error bounds for approximation by picewise polynomials. These constants play an important role in the numerical verification method of solutions for obstacle problems by using finite element methods.
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References
R.Glowinski,Numerical Methods for Nonlinear Variational Problems, Springer, New York, (1984).
M.T.Nakao,A numerical verification method for the existence of weak solutions for nonlinear boundary value problems, Journal of Math. Analysis and Applications 164(1992), 489–507.
M.T.Nakao, N.Yamamoto and S. Kimura,On best constant in the optimal error estimates for the H0/1-projection into piecewise polynomial spaces, to appear in J.Approximation Theory.
M.T.Nakao, S.H.Lee and C.S.Ryoo,Numerical verification of solutions for elastoplastic torsion problems, to appear in Computers and Mathematics with Applications.
M. Plum,Explicit H 2 -estimates and pointwise bounds for solutions of second order elliptic boundary value problems, Journal of Mathematical Analysis and Applications 165(1992), 36–61.
M. Plum,Computer-Assister Existence Proofs for Two-Point Boundary Value Problems, Computing 46(1991), 19–34.
C.S.Ryoo,A computational verification method of solution with uniqueness for obstacle problems, Bulletin of Informatics and Cybernetics 30(1998), 133–144.
C.S.Ryoo and M.T.Nakao,Numerical verification of solutions for variational inequalities, Numerische Mathematik 81(1998), 305–320.
M.H Schultz,Spline Analysis, Prentice-Hall, London(1973).
N.Yamamoto,A numerical verification method for solutions of boundary value problems with local uniqueness by Banach’s fixed point theorem, to appear in SIAM J. Numer. Anal.
N. Yamamoto and M.T. Nakao,Numerical verifications of solutions for elliptic equations in nonconvex polygonal domains, Numerische Mathematik 65(1993), 503–521.
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Ryoo, C.S. A priori error estimates for the finite element approximation of an obstacle problem. Korean J. Comput. & Appl. Math 7, 175–181 (2000). https://doi.org/10.1007/BF03009935
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DOI: https://doi.org/10.1007/BF03009935