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With the development of multi-layer elastic systems in the field of engineering mechanics, the corresponding variational inequality theory and algorithm design have received more attention and research. In this study, a class of equivalent…

Numerical Analysis · Mathematics 2024-09-11 Zhizhuo Zhang , Mikaël Barboteu , Xiaobing Nie , Serge Dumont , Mahmoud Abdel-Aty , Jinde Cao

In the present paper we propose a coupled multigrid method for generalized Stokes flow problems. Such problems occur as subproblems in implicit time-stepping approaches for time-dependent Stokes problems. The discretized Stokes system is a…

Numerical Analysis · Mathematics 2016-01-08 Stefan Takacs

This work develops and analyzes a variational-monolithic unfitted finite element formulation of a linear fluid-structure interaction problem in Eulerian coordinates with a fixed interface. The overall discretization is based on a backward…

Numerical Analysis · Mathematics 2026-03-27 Stefan Frei , Tobias Knoke , Marc C. Steinbach , Anne-Kathrin Wenske , Thomas Wick

We develop a Nitsche fictitious domain method for the Stokes problem starting from a stabilized Galerkin finite element method with low order elements for both the velocity and the pressure. By introducing additional penalty terms for the…

Numerical Analysis · Mathematics 2012-06-12 Andre Massing , Mats G. Larson , Anders Logg , Marie E. Rognes

We present a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. We consider a symmetric integral form of these nonlocal equations defined on general geometries and in arbitrary bounded…

Numerical Analysis · Mathematics 2023-06-28 Wenyu Lei , George Turkiyyah , Omar Knio

This paper develops and analyzes a fully discrete finite element method for a class of semilinear stochastic partial differential equations (SPDEs) with multiplicative noise. The nonlinearity in the diffusion term of the SPDEs is assumed to…

Numerical Analysis · Mathematics 2018-11-22 Xiaobing Feng , Yukun Li , Yi Zhang

A high order cut finite element method is formulated for solving the elastic wave equation. Both a single domain problem and an interface problem are treated. The boundary or interface are allowed to cut through the background mesh. To…

Numerical Analysis · Mathematics 2018-04-03 Simon Sticko , Gustav Ludvigsson , Gunilla Kreiss

We consider a Stokes problem posed on a 2D surface embedded in a 3D domain. The equations describe an equilibrium, area-preserving tangential flow of a viscous surface fluid and serve as a model problem in the dynamics of material…

Numerical Analysis · Mathematics 2018-01-23 Maxim A. Olshanskii , Annalisa Quaini , Arnold Reusken , Vladimir Yushutin

We consider the discretization of a stationary Stokes interface problem in a velocity-pressure formulation. The interface is described implicitly as the zero level of a scalar function as it is common in level set based methods. Hence, the…

Numerical Analysis · Mathematics 2016-05-16 Philip Lederer , Carl-Martin Pfeiler , Christoph Wintersteiger , Christoph Lehrenfeld

We model incompressible flows with an adaptive stabilized finite element method Stokes flows, which solves a discretely stable saddle-point problem to approximate the velocity-pressure pair. Additionally, this saddle-point problem delivers…

Numerical Analysis · Mathematics 2020-11-19 Felix Kyburg , Sergio Rojas , Victor M. Calo

This paper is concerned with fully discrete mixed finite element approximations of the time-dependent stochastic Stokes equations with multiplicative noise. A prototypical method, which comprises of the Euler-Maruyama scheme for time…

Numerical Analysis · Mathematics 2020-04-28 Xiaobing Feng , Hailong Qiu

Motivated by the need for efficient and accurate simulation of the dynamics of the polar ice sheets, we design high-order finite element discretizations and scalable solvers for the solution of nonlinear incompressible Stokes equations. We…

Numerical Analysis · Computer Science 2015-11-05 Tobin Isaac , Georg Stadler , Omar Ghattas

Nitsche's method is a numerical approach that weakly enforces boundary conditions for partial differential equations. In recent years, Nitsche's method has experienced a revival owing to its natural application in modern computational…

Numerical Analysis · Mathematics 2025-05-13 Hiroki Ishizaka

This paper explores the application of the multiscale finite element method (MsFEM) to address steady-state Stokes-Darcy problems with BJS interface conditions in highly heterogeneous porous media. We assume the existence of multiscale…

Numerical Analysis · Mathematics 2024-01-09 Yachen Hong , Wenhan Zhang , Lina Zhao , Haibiao Zheng

The goal of this paper is to introduce a simple finite element method to solve the Stokes and the Navier-Stokes equations. This method is in primal velocity-pressure formulation and is so simple such that both velocity and pressure are…

Numerical Analysis · Mathematics 2016-10-19 Lin Mu , Xiu Ye

The paper addresses stability and finite element analysis of the stationary two-phase Stokes problem with a piecewise constant viscosity coefficient experiencing a jump across the interface between two fluid phases. We first prove a priori…

Numerical Analysis · Mathematics 2020-04-23 Ernesto Cáceres , Johnny Guzmán , Maxim Olshanskii

We study a higher-order surface finite element (SFEM) penalty-based discretization of the tangential surface Stokes problem. Several discrete formulations are investigated which are equivalent in the continuous setting. The impact of the…

Numerical Analysis · Mathematics 2025-03-11 Hanne Hardering , Simon Praetorius

We present guidelines for deriving new Nitsche Finite Element Methods to enforce equality and inequality constraints that act on the value of the unknown mechanical quantity. We first formulate the problem as a stabilized finite element…

Numerical Analysis · Mathematics 2026-05-01 Tom Gustafsson , Antti Hannukainen , Vili Kohonen , Juha Videman

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

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