Analysis of Mixed Methods Using Mesh Dependent Norms.
Abstract
This paper presents a new approach to the analysis of mixed methods for the approximate solution of 4th order elliptic boundary value problems. In this approach one introduces a pair of mesh dependent norms and proves the approximation method is stable with respect to these norms. The error estimates then follow in a direct manner. In a mixed method, one introduces an auxiliary variable, usually representing another physically important quantity, and writes the differential equation as a lower order system. One then considers Ritz-Galerkin approximation schemes based on a variational formulation of this lower order system, thereby obtaining direct approximations to both the original and auxiliary variables. Three particular mixed methods for the approximate solution of the biharmonic problem are examined in detail.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1979
- Accession Number
- ADA079738
Entities
People
- I. Babuška
- J. Osborn
- J. Pitkaranta
Organizations
- University of Wisconsin–Madison