Analysis of Finite Element Methods for Second Order Boundary Value Problems Using Mesh Dependent Norms.
Abstract
This paper presents a new approach to the analysis of finite element methods based on C-finite elements for the approximate solution of 2nd order boundary value problems in which error estimates are derived directly in terms of two mesh dependent norms that are closely related to the L2 norm and to the 2nd order Sobolev norm, respectively, and in which there is no assumption of quasi-uniformity on the mesh family. This is in contrast to the usual analysis in which error estimates are first derived in the 1st order Sobolev norm and subsequently are derived in the L2 norm and in the 2nd order Sobolev norm - the 2nd order Sobolev norm estimates being obtained under the assumption that the functions in the underlying approximating subspaces lie in the 2nd order Sobolev space and that the mesh family is quasi-uniform. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1979
- Accession Number
- ADA068902
Entities
People
- I. Babuška
- J. Osborn
Organizations
- University of Wisconsin–Madison