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Domain decomposition with local mesh refinement. (English) Zbl 0756.65045
The authors present a preconditioned Krylov iterative algorithm which can be used to solve systems of linear equations arising from the discretization of partial differential equations. The main feature of their method lies in the combined admissibility of domain decomposition and local mesh refinements.
By way of illustration, the method is applied to several 2-dimensional elliptic boundary value problems. The results are compared with those obtained by other widely used computational methods.

MSC:
65F10 Iterative numerical methods for linear systems
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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