An unfitted hybrid high-order method for the Stokes interface problem

Burman, Erik; Delay, Guillaume; Ern, Alexandre

doi:10.1093/imanum/draa059

Cited by 18 publications

(14 citation statements)

References 32 publications

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“…Recently, immersed methods have received special attention, both in the context of HHO and HDG formulations. More precisely, unfitted HHO methods relying on a cell agglomeration procedure to remedy small cut instabilities are analysed for scalar and vectorial second-order elliptic problems in [39,40]. In the framework of HDG, Poisson interface problems are treated in [121] by means of an unfitted method introducing appropriately defined ansatz functions in the vicinity of the interface.…”

Section: Interface Problems and Immersed Discretisationsmentioning

confidence: 99%

HDGlab: An Open-Source Implementation of the Hybridisable Discontinuous Galerkin Method in MATLAB

Giacomini

Sevilla

Huerta

2020

Arch Computat Methods Eng

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This paper presents , an open source MATLAB implementation of the hybridisable discontinuous Galerkin (HDG) method. The main goal is to provide a detailed description of both the HDG method for elliptic problems and its implementation available in . Ultimately, this is expected to make this relatively new advanced discretisation method more accessible to the computational engineering community. presents some features not available in other implementations of the HDG method that can be found in the free domain. First, it implements high-order polynomial shape functions up to degree nine, with both equally-spaced and Fekete nodal distributions. Second, it supports curved isoparametric simplicial elements in two and three dimensions. Third, it supports non-uniform degree polynomial approximations and it provides a flexible structure to devise degree adaptivity strategies. Finally, an interface with the open-source high-order mesh generator is provided to facilitate its application to practical engineering problems.

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Section: Interface Problems and Immersed Discretisationsmentioning

confidence: 99%

HDGlab: An Open-Source Implementation of the Hybridisable Discontinuous Galerkin Method in MATLAB

Giacomini

Sevilla

Huerta

2020

Arch Computat Methods Eng

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“…It is well known that a crucial aspect involving the stability of the numerical scheme associated with the Stokes problem is the inf-sup condition that establishes a constraint in the choice of the velocity and pressure discrete spaces; see, e.g, [13,19]. This aspect, in the context of polygonal methods, is still under investigation and only few results are present in the literature; see, e.g., [2,20,29,31,33,65,68].…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Polytopic Discontinuous Galerkin Approximations of the Stokes Problem with Applications to Fluid–Structure Interaction Problems

et al. 2021

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We present a stability analysis of the Discontinuous Galerkin method on polygonal and polyhedral meshes (PolyDG) for the Stokes problem. In particular, we analyze the discrete inf-sup condition for different choices of the polynomial approximation order of the velocity and pressure approximation spaces. To this aim, we employ a generalized inf-sup condition with a pressure stabilization term. We also prove a priori hp-version error estimates in suitable norms. We numerically check the behaviour of the inf-sup constant and the order of convergence with respect to the mesh configuration, the mesh-size, and the polynomial degree. Finally, as a relevant application of our analysis, we consider the PolyDG approximation for a 2D fluid-structure interaction problem and we numerically explore the stability properties of the method.

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“…See [15,18,24,27,35,45] for the application of CutFEM or Nitsche-XFEM to approximate two-phase flows. Finally, recently proposed unfitted methods are a hybrid high-order method [10] and an enriched finite element/level-set method [26].…”

Section: Introductionmentioning

confidence: 99%

“…Two-phase flow problems with high contrast for the viscosity are known to be especially challenging. While some authors test different viscosity ratios but do not comment on the effects of high contrast on the numerics [15,26,46], others show or prove that their method is robust for all viscosity ratios [27,10,30,37,45]. In other cases, numerical parameters, like the penalty parameters, are adjusted to take into account large differences in the viscosity [18].…”

Section: Introductionmentioning

confidence: 99%

An unfitted finite element method for two-phase Stokes problems with slip between phases

Olshanskii¹,

Quaini²,

Sun³

2021

Preprint

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We present an isoparametric unfitted finite element approach of the CutFEM or Nitsche-XFEM family for the simulation of two-phase Stokes problems with slip between phases. For the unfitted generalized Taylor-Hood finite element pair P k+1 − P k , k ≥ 1, we show an infsup stability property with a stability constant that is independent of the viscosity ratio, slip coefficient, position of the interface with respect to the background mesh and, of course, mesh size. In addition, we prove stability and optimal error estimates that follow from this infsup property. We provide numerical results in two and three dimensions to corroborate the theoretical findings and demonstrate the robustness of our approach with respect to the contrast in viscosity, slip coefficient value, and position of the interface relative to the fixed computational mesh.

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An unfitted hybrid high-order method for the Stokes interface problem

Cited by 18 publications

References 32 publications

HDGlab: An Open-Source Implementation of the Hybridisable Discontinuous Galerkin Method in MATLAB

HDGlab: An Open-Source Implementation of the Hybridisable Discontinuous Galerkin Method in MATLAB

Stability Analysis of Polytopic Discontinuous Galerkin Approximations of the Stokes Problem with Applications to Fluid–Structure Interaction Problems

An unfitted finite element method for two-phase Stokes problems with slip between phases

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