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The optimal design task of this paper seeks the distribution of two materials of prescribed amounts for maximal torsion stiffness of an infinite bar of given cross section. This example of relaxation in topology optimisation leads to a degenerate convex minimisation problem E (v) := ˆ Ω ϕ 0 (|∇v|) dx − ˆ Ω f v dx for v ∈ V := H 1 0 (Ω) with possibly… (More)

This paper presents an optimal nonconforming adaptive finite element algorithm and proves its quasi-optimal complexity for the Stokes equations with respect to natural approximation classes. The proof does not explicitly involve the pressure variable and follows from a novel discrete Helmholtz decomposition of devi-atoric functions.

- D I S S E RTAT, Hella Andrea Rabus, Jan-Hendrik Olbertz, Elmar Kulke, Carsten Carstensen, Susanne C. Brenner +1 other
- 2014

Various applications in computational fluid dynamics and solid mechanics motivate the development of reliable and efficient adaptive algorithms for nonstandard finite element methods (FEMs), such as mixed and nonconforming ones. Standard adaptive finite element algorithms consist of the iterative loop of the basic steps Solve, Estimate, Mark and Refine. To… (More)

- HELLA RABUS
- 2012

The optimal design task of this paper seeks the distribution of two materials of prescribed amounts for maximal torsion stiffness of an infinite bar of a given cross section. This example of relaxation in topology optimization leads to a degenerate convex minimization problem E (v) := Ω ϕ 0 (|∇v|) dx − Ω fv dx for v ∈ V := H 1 0 (Ω) with possibly multiple… (More)

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