Fast adaptive composite grid (FAC) methods: Theory for the variational case. (English) Zbl 0552.65071

McCormick, S.

Defect correction methods. Theory and applications, Comput. Suppl. 5, 115-121 (1984).

[For the entire collection see Zbl 0545.00019.]
Consider a composite grid consisting of nested grids \(D\subset {\mathcal D}\), D coarse and \({\mathcal D}\) locally refined. Let a selfadjoint elliptic boundary value problem be discretized on \({\mathcal D}\). The resulting linear system is solved by iterating between the solution of a Galerkin approximation on D of the error equation, and a block relaxation step on all variables in the refined part of \({\mathcal D}\). The convergence factor of this process is estimated in the discrete energy norm. Conditions implying h-independent convergence can be verified from usual regularity and approximation assumptions.

Reviewer: J.Mandel

MSC:

65N22	Numerical solution of discretized equations 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:

refinement; iterative method; local defect correction; convergence estimates; Galerkin approximation; block relaxation

Citations:

Zbl 0545.00019