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On an adaptive grid refining technique for finite element approximations. (English) Zbl 0616.65107

This paper considers a family of finite element spaces and minimizes an energy functional over each space. The space which allows the lowest energy is considered ”optimal”. Such a family is constructed by starting with an initial ”triangulation” and refining one or more ”triangles” at a time. An estimate is given for the profit in energy gained by refining a triangle and a discrete optimization problem is set up which determines the optimal refinement strategy according to a prescribed bound of the costs. This permits the construction of the final grid by using as few as possible intermediate grids. Instead of solving the original optimization problem a partially dualized form of it is set up which produces a nearly optimal solution and can be solved very efficiently.
Reviewer: I.N.Katz

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods 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
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