| 1. |
- Arndt, Daniel, et al.
(author)
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The deal. II library, Version 9.3
- 2021
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In: Journal of Numerical Mathematics. - : Walter de Gruyter. - 1570-2820 .- 1569-3953. ; 29:3, s. 171-186
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Journal article (peer-reviewed)abstract
- This paper provides an overview of the new features of the finite element library deal . II, version 9.3.
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| 2. |
- Arndt, Daniel, et al.
(author)
-
The deal.II library, Version 9.4
- 2022
-
In: Journal of Numerical Mathematics. - : Walter de Gruyter. - 1570-2820 .- 1569-3953. ; 30:3, s. 231-246
-
Journal article (peer-reviewed)abstract
- This paper provides an overview of the new features of the finite element library deal.II, version 9.4.
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| 3. |
- Axelsson, Owe, et al.
(author)
-
An efficient preconditioning method for state box-constrained optimal control problems
- 2018
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In: Journal of Numerical Mathematics. - : Walter de Gruyter GmbH. - 1570-2820 .- 1569-3953. ; 26, s. 185-207
-
Journal article (peer-reviewed)abstract
- An efficient preconditioning technique used earlier for two-by-two block matrix systems with square matrix blocks is shown to be applicable also for a state variable box-constrained optimal control problem. The problem is penalized by a standard regularization term for the control variable and for the box-constraint, using a Moreau–Yosida penalization method. It is shown that there occur very few nonlinear iteration steps and also few iterations to solve the arising linearized equations on the fine mesh. This holds for a wide range of the penalization and discretization parameters. The arising nonlinearity can be handled with a hybrid nonlinear-linear procedure that raises the computational efficiency of the overall solution method.
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| 4. |
- Boiveau, Thomas, et al.
(author)
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Fictitious domain method with boundary value correction using penalty-free Nitsche method
- 2018
-
In: Journal of Numerical Mathematics. - : Walter de Gruyter. - 1570-2820 .- 1569-3953. ; 26:2, s. 77-95
-
Journal article (peer-reviewed)abstract
- In this paper, we consider a fictitious domain approach based on a Nitsche type method without penalty. To allow for high order approximation using piecewise affine approximation of the geometry we use a boundary value correction technique based on Taylor expansion from the approximate to the physical boundary. To ensure stability of the method a ghost penalty stabilization is considered in the boundary zone. We prove optimal error estimates in the H1-norm and estimates suboptimal by ?(h1/2) in the L2-norm. The suboptimality is due to the lack of adjoint consistency of our formulation. Numerical results are provided to corroborate the theoretical study.
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| 5. |
- Hansbo, Peter F G, 1959, et al.
(author)
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An adaptive low-order FE-scheme for Stokes flow with cavitation
- 2010
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In: Journal of Numerical Mathematics. - 1570-2820 .- 1569-3953. ; 18:3, s. 177-185
-
Journal article (peer-reviewed)abstract
- In this note we derive a posteriori error bounds for FE-discretisations for a fluid problem with cavitation. The underlying model is the Stokes system together with an inequality constraint for the pressure. In order to avoid suboptimal behavior of the error bounds we propose to employ a Lagrange setting yielding an improved estimate. Numerical tests confirm our theoretical results.
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