Incremental unknowns for solving partial differential equations. (English) Zbl 0712.65103

Incremental unknowns were introduced as a means to approximate fractal attractors by using finite differences. In the case of linear elliptic problems, the utilization of incremental unknowns provides a new way for solving such problems using several levels of discretization; the method is similar but different from the classical multigrid methods.
In this article we describe the utilization of incremental unknowns for solving a Laplace operator in dimensions one and two. We provide some theoretical results concerning two-level approximations, and we present the numerical tests done with the multi-level approximations. The tests show that for this problem, the conjugate gradient method in conjunction with the incremental unknowns provides a method which has the efficiency comparable to the V-cycle multigrid method.
Reviewer: M.Chen


65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
35J25 Boundary value problems for second-order elliptic equations
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