Previous |  Up |  Next


external approximations; superconvergence; external method; Galerkin method; rate of convergence; two-point boundary value problems
The superconvergence property of a certain external method for solving two point boundary value problems is established. In the case when piecewise polynomial spaces are applied, it is proved that the convergence rate of the approximate solution at the knot points can exceed the global one.
[1] J. P. Aubin: Approximation of elliptic boundary-value problems. Wiley-Interscience, New York, 1972. MR 0478662 | Zbl 0248.65063
[2] C. De Boor B. Swartz: Collocation at Gausian points. SIAM J. Numer. Anal. 10 (1973), 582-606. DOI 10.1137/0710052 | MR 0373328
[3] P. Ciarlet: The finite element method for elliptic problems. North-Holland, Publishing Company (1978). MR 0520174 | Zbl 0383.65058
[4] J. Douglas, Jr. T. Dupont: Collocation method for parabolic equations in a single space variable. Lecture Notes in Math., 385 (1974). MR 0483559
[5] J. Douglas, Jr. T. Dupont: Some superconvergence results for Galerkin methods for the approximate solution of two-point boundary problems. - Topics in numerical analysis, ed. J.J.M.F. Miller, pp. 89-92 (1973). MR 0366044
[6] P. J. Davis: Interpolation and approximation. Blaisdell Publishing Company (1963). MR 0157156 | Zbl 0111.06003
[7] M. Křížek P. Neittaanmäki: Superconvergence phenomenon in the finite element method arising from averaging gradients. Numer. Math. 45 (1984), pp. 105-116. DOI 10.1007/BF01379664 | MR 0761883
[8] T. Regińska: Superconvergence of eigenvalue external approximation for ordinary differential operators. IMA Jour. Numer. Anal. 6 (1986), pp. 309-323. DOI 10.1093/imanum/6.3.309 | MR 0967671
[9] M. Zlámal: Some superconvergence results in the finite element method. - Mathematical Aspects of f.e.m., Lecture Notes 606 (1977), pp. 353 - 362. DOI 10.1007/BFb0064473 | MR 0488863
Partner of
EuDML logo