DOpElib: Differential Equations and Optimization Environment; A Goal Oriented Software Library for Solving PDEs and Optimization Problems with PDEs

Goll, Christian; Wick, Thomas; Wollner, Winnifried

doi:10.11588/ans.2017.2.11815

Archive of Numerical Software 2017

DOI: 10.11588/ans.2017.2.11815

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DOpElib: Differential Equations and Optimization Environment; A Goal Oriented Software Library for Solving PDEs and Optimization Problems with PDEs

Christian Goll

Thomas Wick

Winnifried Wollner

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Cited by 2 publications

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Gradient Robust Mixed Methods for Nearly Incompressible Elasticity

Basava

Wollner

2023

J Sci Comput

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Within the last years pressure robust methods for the discretization of incompressible fluids have been developed. These methods allow the use of standard finite elements for the solution of the problem while simultaneously removing a spurious pressure influence in the approximation error of the velocity of the fluid, or the displacement of an incompressible solid. To this end, reconstruction operators are utilized mapping discretely divergence free functions to divergence free functions. This work shows that the modifications proposed for Stokes equation by Linke (Comput Methods Appl Mech Eng 268:782–800, 2014) also yield gradient robust methods for nearly incompressible elastic materials without the need to resort to discontinuous finite elements methods as proposed in Fu et al. (J Sci Comput 86(3):39–30, 2021).

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Gradient Robust Mixed Methods for Nearly Incompressible Elasticity

Basava

Wollner

2023

J Sci Comput

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A priori error estimates for a linearized fracture control problem

Mohammadi

Wollner

2020

Optim Eng

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A control problem for a linearized time-discrete regularized fracture propagation process is considered. The discretization of the problem is done using a conforming finite element method. In contrast to many works on discretization of PDE constrained optimization problems, the particular setting has to cope with the fact that the linearized fracture equation is not necessarily coercive. A quasi-best approximation result will be shown in the case of an invertible, though not necessarily coercive, linearized fracture equation. Based on this a priori error estimates for the control, state, and adjoint variables will be derived.

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DOpElib: Differential Equations and Optimization Environment; A Goal Oriented Software Library for Solving PDEs and Optimization Problems with PDEs

Cited by 2 publications

References 6 publications

Gradient Robust Mixed Methods for Nearly Incompressible Elasticity

Gradient Robust Mixed Methods for Nearly Incompressible Elasticity

A priori error estimates for a linearized fracture control problem

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