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**The fast adaptive composite grid (FAC) method for elliptic equations.**
*(English)*
Zbl 0594.65078

The paper provides some theoretical foundation for various two-level versions of the fast adaptive composite grid method (FAC) earlier reported by one of the present authors. FAC is a discretization and solution method designed to achieve efficient local resolution by constructing the discretization based on various regular grids and using these grids as a basis for fast solution of elliptic partial differential equations. Its basic computational objective is to solve a ”good” discretization on an irregular grid by way of regular grids only with the assumption that both discretization and solution on regular grids are comparatively easy.

Several issues that are important for practical implementation of FAC are also discussed in the present paper. Numerical experiments with FAC include application to two types of problems, one a modification of Poisson’s equation on a staggered grid with a re-entrant boundary and the other a singular aligned grid discretization of the so-called five-spot problem in oil reservoir simulation.

Several issues that are important for practical implementation of FAC are also discussed in the present paper. Numerical experiments with FAC include application to two types of problems, one a modification of Poisson’s equation on a staggered grid with a re-entrant boundary and the other a singular aligned grid discretization of the so-called five-spot problem in oil reservoir simulation.

Reviewer: P.Onumanyi

### MSC:

65N22 | Numerical solution of discretized equations for boundary value problems involving PDEs |

65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |

35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |

76S05 | Flows in porous media; filtration; seepage |