Random geometries for optimal control PDE problems based on fictitious domain FEMs and cut elements

Aretaki, Aikaterini; Karatzas, Efthymios N.

doi:10.1016/j.cam.2022.114286

Cited by 4 publications

(1 citation statement)

References 56 publications

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“…We note that in practice, the condition number for arbitrarily shaped boundary elements discontinuous Galerkin methods to solve Stokes problem is typically very large. The employment of efficient multigrid preconditioners for such cases, is left as a further challenge, see also the works [1], [22]. We also clarify that for the curved boundary elements, the current implementation performs quadrature by a sufficiently fine sub-triangulation approximating properly the curved element.…”

Section: Numerical Experiments/convergence Testsmentioning

confidence: 93%

hp-version analysis for arbitrarily shaped elements on the boundary discontinuous Galerkin method for Stokes systems

Karatzas¹

2023

Preprint

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In the present work, we examine and analyze an alternative of the unfitted mesh finite element method improved by omitting computationally expensive, especially for fluids, stabilization type of penalty onto the boundary area, namely the so-called ghost penalty. This approach is based on the discontinuous Galerkin method, enriched by arbitrarily shaped boundary elements techniques. In this framework, we examine a stationary Stokes fluid system and we prove the inf/sup condition, the hp-a priori error estimates, to our knowledge for the first time in the literature, while we investigate the optimal convergence rates numerically. This approach recovers and integrates the flexibility and superiority of the unfitted methods whenever geometrical deformations are taking place, combined with the efficiency of the hp-version techniques based on arbitrarily shaped elements on the boundary.

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Section: Numerical Experiments/convergence Testsmentioning

confidence: 93%

hp-version analysis for arbitrarily shaped elements on the boundary discontinuous Galerkin method for Stokes systems

Karatzas¹

2023

Preprint

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Equal Higher Order Analysis of an Unfitted Discontinuous Galerkin Method for Stokes Flow Systems

2022

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Boundary and distributed optimal control for a population dynamics PDE model with discontinuous in time Galerkin FEM schemes

Karatzas

2024

Computers & Mathematics with Applications

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Random geometries for optimal control PDE problems based on fictitious domain FEMs and cut elements

Cited by 4 publications

References 56 publications

hp-version analysis for arbitrarily shaped elements on the boundary discontinuous Galerkin method for Stokes systems

hp-version analysis for arbitrarily shaped elements on the boundary discontinuous Galerkin method for Stokes systems

Equal Higher Order Analysis of an Unfitted Discontinuous Galerkin Method for Stokes Flow Systems

Boundary and distributed optimal control for a population dynamics PDE model with discontinuous in time Galerkin FEM schemes

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