Glowinski, Roland; Pan, Tsorng-Whay Error estimates for fictitious domain/penalty/finite element methods. (English) Zbl 0770.65066 Calcolo 29, No. 1-2, 125-141 (1992). Using fictitious domain/ penalty methods error estimates for the finite element method for elliptic problems with Neumann boundary conditions are derived. Numerical examples are also given. Reviewer: S.Filippi (Gießen) Cited in 12 Documents MSC: 65N15 Error bounds for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations Keywords:method of fictitious domains; penalty methods; error estimates; finite element method; Numerical examples PDFBibTeX XMLCite \textit{R. Glowinski} and \textit{T.-W. Pan}, Calcolo 29, No. 1--2, 125--141 (1992; Zbl 0770.65066) Full Text: DOI References: [1] B. L. Buzbee, F. W. Dorr, J. A. George, G. H. Golub,The direct solution of the discrete Poisson equation on irregular regions, SIAM J. Numer. Anal. 8 (1971), 722–736. · Zbl 0231.65083 · doi:10.1137/0708066 [2] P. G. Ciarlet,The finite element methods for elliptic problems (1987), North-Holland, Amsterdam. [3] D. Gilbarg, N. S. Trudinger,Elliptic partial differential equations of second order (1983), Springer-Verlag, Berlin. · Zbl 0562.35001 [4] R. Glowinski, J. Periaux, M. Ravachol, T. W. Pan, R. O. Wells, X. Zhou, Wavelet methods in computational fluid dynamics, Proceedings of the NASA Langley Conference on Computational Dynamics in the Nineties, Hampton, VA, USA, October, 1991, Springer-Verlag. (to appear). [5] J. Nečas,Les méthodes directes en théorie des équations elliptiques (1967), Masson, Paris. [6] D. P. Young, R. G. Melvin, M. B. Bieterman, F. T. Johnson, S. S. Samanth, J. E. Bussoletti,A locally refined rectangular grid finite element method. Application to Computational Physics, J. Comput. Phys. 92 (1991), 1–66. · Zbl 0709.76078 · doi:10.1016/0021-9991(91)90291-R This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.