The finite element method with penalty
Open Access
- 1 January 1973
- journal article
- Published by American Mathematical Society (AMS) in Mathematics of Computation
- Vol. 27 (122), 221-228
- https://doi.org/10.1090/s0025-5718-1973-0351118-5
Abstract
An application of the penalty method to the finite element method is analyzed. For a model Poisson equation with homogeneous Dirichlet boundary conditions, a variational principle with penalty is discussed. This principle leads to the solution of the Poisson equation by using functions that do not satisfy the boundary condition. The rate of convergence is discussed.Keywords
This publication has 7 references indexed in Scilit:
- Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sindAbhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, 1971
- The Rate of Convergence for the Finite Element MethodSIAM Journal on Numerical Analysis, 1971
- ON THE NUMERICAL SOLUTION OF ELLIPTIC BOUNDARY VALUE PROBLEMS BY LEAST SQUARES APPROXIMATION OF THE DATA**This research was supported in part by the National Science Foundation under Grant Number NSF-GP-22936.Published by Elsevier ,1971
- THE FINITE ELEMENT METHOD FOR ELLIPTIC DIFFERENTIAL EQUATIONS**This research was supported in part by the National Science Foundation under Grant No, NSF GU 2061 and in part by the Atomic Energy Commission under Contract No. AEC AT(40–1) 3443/3.Published by Elsevier ,1971
- SOME ASPECTS OF THE METHOD OF THE HYPERCIRCLE APPLIED TO ELLIPTIC VARIATIONAL PROBLEMS**Sponsored by the Mathematics Research Center, United States Army, Madison, Wisconsin, under Contract No. DA-31-124-ARO-D-462.Published by Elsevier ,1971
- Error-bounds for finite element methodNumerische Mathematik, 1971
- The finite element method for elliptic equations with discontinuous coefficientsComputing, 1970