On the Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems in Two and One Dimensions
Open Access
- 1 January 1983
- journal article
- Published by JSTOR in Mathematics of Computation
- Vol. 40 (161) , 47-89
- https://doi.org/10.2307/2007363
Abstract
Second order elliptic boundary value problems which are allowed to degenerate into zero order equations are considered. The behavior of the ordinary Galerkin finite element method without special arrangements to treat singularities is studied as the problem ranges from true second order to singularly perturbed.Keywords
This publication has 11 references indexed in Scilit:
- On the Quasi-Optimality in $L_\infty$ of the $\overset{\circ}{H}^1$-Projection into Finite Element Spaces*Mathematics of Computation, 1982
- A quasioptimal estimate in piecewise polynomial Galerkin approximation of parabolic problemsPublished by Springer Nature ,1982
- A-Posteriori Error Estimates and Adaptive Finite Element Computations for Singularly Perturbed one Space Dimensional Parabolic EquationsNorth-Holland Mathematics Studies, 1981
- Maximum norm stability and error estimates in parabolic finite element equationsCommunications on Pure and Applied Mathematics, 1980
- The Finite Element Method for Elliptic ProblemsJournal of Applied Mechanics, 1978
- Interior Maximum Norm Estimates for Finite Element MethodsMathematics of Computation, 1977
- Singular perturbation problems for linear elliptic differential operators of arbitrary order. I. Degeneration to elliptic operatorsJournal of Mathematical Analysis and Applications, 1975
- Error estimates for a Galerkin method for a class of model equations for long wavesNumerische Mathematik, 1974
- Perturbations Singulières dans les Problèmes aux Limites et en Contrôle OptimalPublished by Springer Nature ,1973
- On Finite Element MatricesSIAM Journal on Numerical Analysis, 1972