Interacting with the subgrid world. (English) Zbl 0952.65092

Brezzi, F.

Griffiths, D. F. (ed.) et al., Numerical analysis 1999. Proceedings of the 18th Dundee biennial conference, Univ. of Dundee, GB, June 29th - July 2nd, 1999. Boca Raton, FL: Chapman & Hall/ CRC. Chapman Hall/CRC Res. Notes Math. 420, 69-82 (2000).

Summary: In a number of applications, subgrid scales cannot be neglected. Sometimes, they are just a spurious by-product of a discretized scheme that lacks the necessary stability properties. In other cases, they are related to physical phenomena that actually take place on a very small scale but still have an important effect on the solution. We discuss here an attempt to recover information on the subgrid scales, by trying to simulate their effects on the computable ones.
For the entire collection see [Zbl 0938.00012].

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12	Stability and convergence of numerical methods for boundary value problems involving PDEs
65N50	Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations

Keywords:

finite element method; second-order elliptic equations; subgrid scales; stability