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This work presents a new conforming stabilized virtual element method for the generalized Boussinesq equation with temperature-dependent viscosity and thermal conductivity. A gradient-based local projection stabilization method is…

Numerical Analysis · Mathematics 2025-12-29 Sudheer Mishra , Sundararajan Natarajan , Natarajan E

In this paper, we propose a new stabilizer free and pressure robust WG method for the Stokes equations with super-convergence on polytopal mesh in the primary velocity-pressure formulation. Convergence rates with one order higher than the…

Numerical Analysis · Mathematics 2020-11-04 Lin Mu , Xiu Ye , Shangyou Zhang

In this work we introduce and analyze a novel Hybrid High-Order method for the steady incompressible Navier-Stokes equations. The proposed method is inf-sup stable on general polyhedral meshes, supports arbitrary approximation orders, and…

Numerical Analysis · Mathematics 2018-02-26 Daniele A. Di Pietro , Stella Krell

In a recent work [10], we have introduced a pressure-robust Hybrid High-Order method for the numerical solution of the incompressible Navier-Stokes equations on matching simplicial meshes. Pressure-robust methods are characterized by error…

Numerical Analysis · Mathematics 2026-01-22 Daniel Castanon Quiroz , Daniele A. Di Pietro

Pressure Poisson equation (PPE) reformulations of the incompressible Navier-Stokes equations (NSE) replace the incompressibility constraint by a Poisson equation for the pressure and a suitable choice of boundary conditions. This yields a…

Numerical Analysis · Mathematics 2023-08-16 Rodolfo Ruben Rosales , Benjamin Seibold , David Shirokoff , Dong Zhou

A stabilized finite element method is introduced for the simulation of time-periodic creeping flows, such as those found in the cardiorespiratory systems. The new technique, which is formulated in the frequency rather than time domain,…

Numerical Analysis · Mathematics 2022-11-30 Mahdi Esmaily

We develop arbitrarily high-order, stationarity-preserving stabilized finite element methods for multidimensional nonlinear hyperbolic balance laws on Cartesian grids. We aim at approximating all the steady states of the problem at hand,…

Numerical Analysis · Mathematics 2026-03-25 Moussa Ziggaf , Davide Torlo , Mario Ricchiuto

This article presents a higher-order spectral element method for the two-dimensional Stokes interface problem involving a piecewise constant viscosity coefficient. The proposed numerical formulation is based on least-squares formulation.…

Numerical Analysis · Mathematics 2025-08-14 Kishore Kumar Naraparaju , Shivangi Joshi , Subhashree Mohapatra

This paper presents the first application of the direct parametrisation method for invariant manifolds to a fully coupled multiphysics problem involving the nonlinear vibrations of deformable structures subjected to an electrostatic field.…

Numerical Analysis · Mathematics 2023-12-25 Attilio Frangi , Alessio Colombo , Alessandra Vizzaccaro , Cyril Touzé

This work proposes a new stabilized $P_1\times P_0$ finite element method for solving the incompressible Navier--Stokes equations. The numerical scheme is based on a reduced Bernardi--Raugel element with statically condensed face bubbles…

Numerical Analysis · Mathematics 2023-04-06 Yuwen Li , Ludmil Zikatanov

We propose some new mixed finite element methods for the time dependent stochastic Stokes equations with multiplicative noise, which use the Helmholtz decomposition of the driving multiplicative noise. It is known [16] that the pressure…

Numerical Analysis · Mathematics 2020-06-09 Xiaobing Feng , Andreas Prohl , Liet Vo

A three-field local projection stabilized finite element method is developed for computations of a 3D-axisymmetric buoyancy driven bubble rising in a liquid column in which either the bubble or the liquid column can be viscoelastic. The…

Fluid Dynamics · Physics 2019-02-19 Jagannath Venkatesan , Sashikumaar Ganesan

Computational formulations for large strain, polyconvex, nearly incompressible elasticity have been extensively studied, but research on enhancing solution schemes that offer better tradeoffs between accuracy, robustness, and computational…

Applied Physics · Physics 2019-10-22 Elias Karabelas , Gundolf Haase , Gernot Plank , Christoph M. Augustin

This paper analyses conforming and nonconforming virtual element formulations of arbitrary polynomial degrees on general polygonal meshes for the coupling of solid and fluid phases in deformable porous plates. The governing equations…

Numerical Analysis · Mathematics 2024-05-01 Rekha Khot , David Mora , Ricardo Ruiz-Baier

In this work we propose, {analyze}, and validate a stabilized finite element method for a flow problem arising from the assessment of {4D Flow Magnetic Resonance Imaging quality}. Starting from the Navier-Stokes equation and splitting its…

Numerical Analysis · Mathematics 2026-01-27 Gabriel Barrenechea , Cristian Cárcamo , Abner Poza

The micropolar Rayleigh-B{\'e}nard convection system, which consists of Navier-Stokes equations, the angular momentum equation, and the heat equation, is a strongly nonlinear, coupled, and saddle point structural multiphysics system. A…

Numerical Analysis · Mathematics 2025-12-03 Ming Cui , Akang Hou , Xiaoyu Dong

Non divergence-free discretisations for the incompressible Stokes problem may suffer from a lack of pressure-robustness characterised by large discretisations errors due to irrotational forces in the momentum balance. This paper argues that…

Numerical Analysis · Mathematics 2020-02-06 Derk Frerichs , Christian Merdon

In this paper we introduce a mixed virtual element method to approximate the solution for the two dimensional generalized Oseen problem. We introduce the pseudostress as an additional unknown, which allows to eliminate the pressure from the…

Numerical Analysis · Mathematics 2026-01-29 Felipe Lepe , Gonzalo Rivera

We present the construction and application of a first order stabilization-free virtual element method to problems in plane elasticity. Well-posedness and error estimates of the discrete problem are established. The method is assessed on a…

Numerical Analysis · Mathematics 2023-03-17 Alvin Chen , N. Sukumar

We present a new high-order accurate computational fluid dynamics model based on the incompressible Navier-Stokes equations with a free surface for the accurate simulation of nonlinear and dispersive water waves in the time domain. The…

Numerical Analysis · Mathematics 2024-06-06 Anders Melander , Max E. Bitsch , Dong Chen , Allan P. Engsig-Karup