Incremental Unknowns for Solving
Partial Differential Equations
Incremental unknowns have been proposed in Temam (1990)
as a method to approximate
fractal attractors by using finite difference approximations of evolution
equations. In the case of linear elliptic problems, the utilization of
incremental unknown methods provides a new way for solving such problems using
several levels of discretization; the method is similar but different from the
classical multigrid method.
In this article we describe the application of incremental unknowns for solving
Laplace equations in dimensions one and two. We provide theoretical results
concerning two-level approximations and we report on numerical tests done with
multi-level approximations.
Min Chen (chen@math.purdue.edu)