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

Abstract We design and analyze a hybrid high-order method on unfitted meshes to approximate the Stokes interface problem. The interface can cut through the mesh cells in a very general fashion. A cell-agglomeration procedure prevents the appearance of small cut cells. Our main results are inf-sup stability and a priori error estimates with optimal convergence rates in the energy norm. Numerical simulations corroborate these results.

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AN OPTIMAL LOW-ORDER LOCKING-FREE FINITE ELEMENT METHOD FOR REISSNER–MINDLIN PLATES

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202598000172 ◽

1998 ◽

Vol 08 (03) ◽

pp. 407-430 ◽

Cited By ~ 44

Author(s):

D. CHAPELLE ◽

R. STENBERG

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Convergence Rates ◽

A Priori ◽

Mindlin Plate ◽

Plate Model ◽

Simple Modification ◽

Optimal Convergence Rates ◽

Priori Error Estimates ◽

Element Method

We propose a simple modification of a recently introduced locking-free finite element method for the Reissner–Mindlin plate model. By this modification, we are able to obtain optimal convergence rates on numerical benchmarks. These results are substantiated by a complete mathematical analysis which provides optimal a priori error estimates.

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Development of a High-Order Method for the Prediction of Low-Pressure Turbine Losses using Quasi-Direct Numerical Simulations

10.20868/upm.thesis.66214 ◽

2020 ◽

Author(s):

Marc Bolinches i Gisbert

Keyword(s):

Numerical Simulations ◽

Low Pressure ◽

High Order ◽

Direct Numerical Simulations ◽

Order Method ◽

High Order Method ◽

Low Pressure Turbine

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Numerical simulations of mixing under supercritical pressures of a shear coaxial injector using a high-order method: effect of outer jet temperature

Progress in Propulsion Physics ◽

10.1051/eucass/201608025 ◽

2016 ◽

Cited By ~ 2

Author(s):

H. Terashima ◽

M. Koshi

Keyword(s):

Numerical Simulations ◽

High Order ◽

Order Method ◽

High Order Method ◽

Method Effect ◽

Shear Coaxial Injector ◽

Coaxial Injector

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Guaranteed lower bounds on eigenvalues of elliptic operators with a hybrid high-order method

Numerische Mathematik ◽

10.1007/s00211-021-01228-1 ◽

2021 ◽

Author(s):

Carsten Carstensen ◽

Alexandre Ern ◽

Sophie Puttkammer

Keyword(s):

Convergence Rates ◽

Sufficient Conditions ◽

High Order ◽

Dirichlet Eigenvalue ◽

Eigenvalue Bounds ◽

High Order Method ◽

Numerical Studies ◽

Gradient Reconstruction ◽

Optimal Convergence Rates ◽

Dirichlet Eigenvalue Problem

AbstractThis paper introduces a novel hybrid high-order (HHO) method to approximate the eigenvalues of a symmetric compact differential operator. The HHO method combines two gradient reconstruction operators by means of a parameter $$0<\alpha <~1$$ 0 < α < 1 and introduces a novel cell-based stabilization operator weighted by a parameter $$0<\beta <\infty $$ 0 < β < ∞ . Sufficient conditions on the parameters $$\alpha $$ α and $$\beta $$ β are identified leading to a guaranteed lower bound property for the discrete eigenvalues. Moreover optimal convergence rates are established. Numerical studies for the Dirichlet eigenvalue problem of the Laplacian provide evidence for the superiority of the new lower eigenvalue bounds compared to previously available bounds.

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Direct numerical simulation of TS-waves over suction panel steps from manufacturing tolerances

CEAS Aeronautical Journal ◽

10.1007/s13272-021-00496-9 ◽

2021 ◽

Author(s):

H. Lüdeke ◽

R. von Soldenhoff

Keyword(s):

Numerical Simulations ◽

Linear Stability ◽

Direct Numerical Simulations ◽

Linear Stability Theory ◽

High Fidelity ◽

Order Method ◽

Direct Simulation ◽

High Order Method ◽

Manufacturing Tolerances ◽

Tollmien Schlichting

AbstractTo determine allowable tolerances between successive suction panels at hybrid laminar wings with suction surfaces, direct numerical simulations of Tollmien–Schlichting waves over different steps are carried out for realistic suction rates on a wind tunnel configuration. Simulations at given suction panel positions over forward and backward facing steps are carried out by the use of a high-order method for the direct simulation of Tollmien–Schlichting wave growth. Comparisons between high-fidelity direct numerical simulations and quick linear stability calculations have shown capabilities and limits of the well-validated linear stability theory design approach.

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