# An ${L}^{\infty}$ estimate and a superconvergence result for a Galerkin method for elliptic equations based on tensor products of piecewise polynomials

Jim Jr. Douglas; Todd Dupont; Mary Fanett Wheeler

- Volume: 8, Issue: R2, page 61-66
- ISSN: 0764-583X

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top## How to cite

topDouglas, Jim Jr., Dupont, Todd, and Wheeler, Mary Fanett. "An $L^\infty $ estimate and a superconvergence result for a Galerkin method for elliptic equations based on tensor products of piecewise polynomials." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 8.R2 (1974): 61-66. <http://eudml.org/doc/193260>.

@article{Douglas1974,

author = {Douglas, Jim Jr., Dupont, Todd, Wheeler, Mary Fanett},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

language = {eng},

number = {R2},

pages = {61-66},

publisher = {Dunod},

title = {An $L^\infty $ estimate and a superconvergence result for a Galerkin method for elliptic equations based on tensor products of piecewise polynomials},

url = {http://eudml.org/doc/193260},

volume = {8},

year = {1974},

}

TY - JOUR

AU - Douglas, Jim Jr.

AU - Dupont, Todd

AU - Wheeler, Mary Fanett

TI - An $L^\infty $ estimate and a superconvergence result for a Galerkin method for elliptic equations based on tensor products of piecewise polynomials

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 1974

PB - Dunod

VL - 8

IS - R2

SP - 61

EP - 66

LA - eng

UR - http://eudml.org/doc/193260

ER -

## References

top- [1] J. H. BRAMBLE and J. E. OSBORN, Rate of convergence estimates for nonselfadjoint eigenvalue approximations, Math. Comp., 27 (1973), 525-549. Zbl0305.65064MR366029
- [2] J. Jr DOUGLAS, and T. DUPONTGalerkin approximations for the two point boundary problem using continuous piecewise-polynomial spaces, Numer. Math.,, 22 (1974), 99-109. Zbl0331.65051MR362922
- [3] J. Jr DOUGLAS, and T. DUPONT, Superconvergence for Galerkin methods for the two point boundary problem via local projections, Numer. Math., 21 (1973), 270-278. Zbl0281.65046MR331798
- [4] J. Jr. DOUGLAS, T. DUPONT and L. WAHLBIN, Optimal L∞ error estimates for Galerkin approximations to solutions of two point boundary problems, to appear. Zbl0306.65053
- [5] J. Jr. DOUGLAS, T. DUPONT and M. F. WHEELER, A quasi-projection approximation applied to Galerkin procedures for parabolic and hyperbolic equations, to appear.
- [6] J. Jr. DOUGLAS, T. DUPONT and M. F. WHEELER, A Galerkin procedure for approximating the flux on the boundary for elliptic and parabolic boundary value problems, this Journal, 47-59. Zbl0315.65063MR359357

## Citations in EuDML Documents

top- Qiding Zhu, A review of two different approaches for superconvergence analysis
- Jinghong Liu, Liu, Wen, Qiding Zhu, Locally pointwise superconvergence of the tensor-product finite element in three dimensions
- Mitsuhiro T. Nakao, Superconvergence of the gradient of Galerkin approximations for elliptic problems

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