The shape of the surface of a liquid inside a cylindrical tube of general cross-section is approximated by the simplest finite element method. Some a priori estimates are obtained for the approximate solution. Then convergence including pointwise estimates is proved as for uniformly elliptic problems. The analysis also covers the case with a volume contraint. Some numerical results are given.
ASJC Scopus subject areas
- Theoretical Computer Science
- Numerical Analysis
- Computer Science Applications
- Computational Theory and Mathematics
- Computational Mathematics