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Optimized tensor-product approximation spaces. (English) Zbl 0969.65107
The authors deal with the construction of finite element spaces for the approximate solution of symmetric elliptic variational problems in Sobolev spaces. They construct operator adapted finite element subspaces with a lower dimension than the standard full-grid spaces. These new approximation spaces preserve the approximation order of the standard full-grid spaces provided that certain additional regularity assumptions are fulfilled.

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65K10 Numerical optimization and variational techniques
49J20 Existence theories for optimal control problems involving partial differential equations
49M15 Newton-type methods
35J25 Boundary value problems for second-order elliptic equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65Y20 Complexity and performance of numerical algorithms
35J20 Variational methods for second-order elliptic equations
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