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The Reynolds equation, combined with the Elrod algorithm for including the effect of cavitation, resembles a nonlinear convection-diffusion-reaction (CDR) equation. Its solution by finite elements is prone to oscillations in…

Numerical Analysis · Mathematics 2023-10-12 Hauke Gravenkamp , Simon Pfeil , Ramon Codina

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

We develop a variational multiscale proper orthogonal decomposition reduced-order model for turbulent incompressible Navier-Stokes equations. The error analysis of the full discretization of the model is presented. All error contributions…

Numerical Analysis · Mathematics 2013-06-03 Traian Iliescu , Zhu Wang

This work introduces a stabilised finite element formulation for the Stokes flow problem with a nonlinear slip boundary condition of friction type. The boundary condition is enforced with the help of an additional Lagrange multiplier and…

Numerical Analysis · Mathematics 2024-05-21 Tom Gustafsson , Juha Videman

A Skeleton-stabilized ImmersoGeometric Analysis technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed formulation fits within the framework of the finite cell method, where essential…

Electrokinetic phenomena in nanopore sensors and microfluidic devices require accurate simulation of coupled fluid-electrostatic interactions in geometrically complex domains with irregular boundaries and adaptive mesh refinement. We…

Numerical Analysis · Mathematics 2026-02-19 Sudheer Mishra , Sundararajan Natarajan , E. Natarajan , Gianmarco Manzini

A projection-based formulation is presented for non-linear model reduction of problems with extreme scale disparity. The approach allows for the selection of an arbitrary, but complete, set of solution variables while preserving the…

Computational Physics · Physics 2021-10-04 Cheng Huang , Christopher R. Wentland , Karthik Duraisamy , Charles Merkle

We introduce a new discretization of a mixed formulation of the incompressible Stokes equations that includes symmetric viscous stresses. The method is built upon a mass conserving mixed formulation that we recently studied. The improvement…

Numerical Analysis · Mathematics 2024-12-20 Jay Gopalakrishnan , Philip L. Lederer , Joachim Schöberl

We present a new stabilization technique for multiscale convection diffusion problems. Stabilization for these problems has been a challenging task, especially for the case with high Peclet numbers. Our method is based on a constraint…

Numerical Analysis · Mathematics 2018-08-01 Eric T. Chung , Yalchin Efendiev , Wing Tat Leung

In this paper, a three-dimensional numerical solver is developed for suspensions of rigid and soft particles and droplets in viscoelastic and elastoviscoplastic (EVP) fluids. The presented algorithm is designed to allow for the first time…

In this work, we explore the application of Stabilization-Free Virtual Element Methods for Neumann boundary Optimal Control Problems in saddle point formulation. The method is proposed for arbitrary polynomial order of accuracy and general…

Numerical Analysis · Mathematics 2026-03-12 Andrea Borio , Francesca Marcon , Maria Strazzullo

This paper studies non inf-sup stable finite element approximations to the evolutionary Navier--Stokes equations. Several local projection stabilization (LPS) methods corresponding to different stabilization terms are analyzed, thereby…

Numerical Analysis · Mathematics 2017-09-27 Javier de Frutos , Bosco García-Archilla , Volker John , Julia Novo

Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially…

Numerical Analysis · Mathematics 2019-08-14 Stefan Klus , Patrick Gelß , Sebastian Peitz , Christof Schütte

The development of blood-handling medical devices, such as ventricular assist devices, requires the analysis of their biocompatibility. Among other aspects, this includes hemolysis, i.e., red blood cell damage. For this purpose,…

Fluid Dynamics · Physics 2024-04-15 Nico Dirkes , Fabian Key , Marek Behr

We study the numerical approximation of advection-diffusion equations with highly oscillatory coefficients and possibly dominant advection terms by means of the Multiscale Finite Element Method. The latter method is a now classical, finite…

Numerical Analysis · Mathematics 2024-11-12 Rutger A. Biezemans , Claude Le Bris , Frédéric Legoll , Alexei Lozinski

We introduce a high-order finite element method for approximating the Vlasov-Poisson equations. This approach employs continuous Lagrange polynomials in space and explicit Runge-Kutta schemes for time discretization. To stabilize the…

Numerical Analysis · Mathematics 2025-03-12 Junjie Wen , Murtazo Nazarov

A recently developed Eulerian finite element method is applied to solve advection-diffusion equations posed on hypersurfaces. When transport processes on a surface dominate over diffusion, finite element methods tend to be unstable unless…

Numerical Analysis · Mathematics 2013-03-26 Maxim A. Olshanskii , Arnold Reusken , Xianmin Xu

In this paper, we discuss a novel higher-order stabilization-free virtual element method for general second-order elliptic eigenvalue problems. Optimal a priori error estimates are derived for both the approximate eigenspace and…

Numerical Analysis · Mathematics 2026-04-07 Liangkun Xu , Shixi Wang , Yidu Yang , Hai Bi

We numerically investigate the possibility of defining stabilization-free Virtual Element (VEM) discretizations of advection-diffusion problems in the advection-dominated regime. To this end, we consider a SUPG stabilized formulation of the…

Numerical Analysis · Mathematics 2023-10-16 Andrea Borio , Martina Busetto , Francesca Marcon

In this article we formulate a stable computational nonlocal poromechanics model for dynamic analysis of saturated porous media. As a novelty, the stabilization formulation eliminates zero-energy modes associated with the original…

Numerical Analysis · Mathematics 2021-03-24 Shashank Menon , Xiaoyu Song