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

Katsouleas, Georgios; Karatzas, Efthymios N.; Aretaki, Aikaterini

doi:10.1007/s10915-022-01823-w

Cited by 1 publication

(2 citation statements)

References 85 publications

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“…In particular, this means that the number of facets we need to cross so that we pass from the aforementioned element K to K ⊂ Ω is bounded. Similar assumptions were made by [2], see also references therein, which ensure that Γ is reasonably resolved by T cov . For the first inequality (4.1) we compose the norm over Ω cov into sums over internal and boundary T cov elements,…”

Section: Stability Estimatesmentioning

confidence: 84%

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

Karatzas¹

2023

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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: Stability Estimatesmentioning

confidence: 84%

“…Proof. Similar to [2], let (u h , p h ) ∈ V h × Q h and note by Corollary 4.6 that there exists w h ∈ V h in (4.21). A matter of fact, there is no loss of generality in setting |||w h ||| V c = p h Ω and then inequality…”

Section: The Previous Expression and Holds Thatmentioning

confidence: 99%

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

Karatzas¹

2023

Preprint

View full text Add to dashboard Cite

show abstract

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

Cited by 1 publication

References 85 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

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