×

An efficient algorithm for elliptic problems with large parameters. (English. Russian original) Zbl 0990.65130

Comput. Math. Math. Phys. 40, No. 3, 383-395 (2000); translation from Zh. Vychisl. Mat. Mat. Fiz. 40, No. 3, 402-415 (2000).
The author considers a finite-element approximation and an iterative solver for a stiff elliptic boundary value problem with large parameters multiplying the highest derivative. The convergence rate of the algorithm does not depend on the spread of the coefficients or the discretization parameter. The efficient performance of the algorithm requires an efficiently invertible preconditioner for the grid Laplace operator.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
35J25 Boundary value problems for second-order elliptic equations
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
PDF BibTeX XML Cite