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We consider a mixed finite element method for approximating the solution of nearly incompressible elasticity and Stokes equations. The finite element method is based on quadrilateral and hexahedral triangulation using primal and dual…

Numerical Analysis · Mathematics 2013-10-23 Bishnu P. Lamichhane

We propose and analyze a finite element method for a semi-stationary Stokes system modeling compressible fluid flow subject to a Navier-slip boundary condition. The velocity (momentum) equation is approximated by a mixed finite element…

Numerical Analysis · Mathematics 2009-04-07 Kenneth H. Karlsen , Trygve K. Karper

A low-order finite element method is constructed and analysed for an incompressible non-Newtonian flow problem with power-law rheology. The method is based on a continuous piecewise linear approximation of the velocity field and piecewise…

Numerical Analysis · Mathematics 2021-07-28 Gabriel R. Barrenechea , Endre Suli

In this paper we study the finite element approximation of systems of $p(\cdot)$-Stokes type, where $p(\cdot)$ is a (non constant) given function of the space variables. We derive --in some cases optimal-- error estimates for finite element…

Numerical Analysis · Mathematics 2017-01-03 Luigi C. Berselli , Dominic Breit , Lars Diening

A priori analysis for a generalized local projection stabilized conforming finite element approximation of Darcy flow and Stokes problems is presented in this paper. A first-order conforming P1 finite element space is used to approximate…

Numerical Analysis · Mathematics 2020-09-02 Deepika Garg , Sashikumaar Ganesan

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

In this work, we develop an adaptive nonconforming finite element algorithm for the numerical approximation of phase-field parameterized topology optimization governed by the Stokes system. We employ the conforming linear finite element…

Numerical Analysis · Mathematics 2026-04-20 Bangti Jin , Jing Li , Yifeng Xu , Shengfeng Zhu

In this paper, we examine a fully-discrete finite element approximation of the unsteady $p(\cdot,\cdot)$-Stokes equations ($i.e.$, $p(\cdot,\cdot)$ is time- and space-dependent), employing a backward Euler step in time and conforming,…

Numerical Analysis · Mathematics 2025-01-03 Luigi C. Berselli , Alex Kaltenbach , Seungchan Ko

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

A nonconforming $P_3$ finite element is constructed by enriching the conforming $P_3$ finite element space with three $P_3$ nonconforming bubbles and six additional $P_4$ nonconforming bubbles, on each tetrahedron. Here the divergence of…

Numerical Analysis · Mathematics 2024-08-21 Xuejun Xu , Shangyou Zhang

The paper shows an inf-sup stability property for several well-known 2D and 3D Stokes elements on triangulations which are not fitted to a given smooth or polygonal domain. The property implies stability and optimal error estimates for a…

Numerical Analysis · Mathematics 2017-04-24 Johnny Guzmán , Maxim Olshanskii

Two nonconforming finite element Stokes complexes starting from the conforming Lagrange element and ending with the nonconforming $P_1$-$P_0$ element for the Stokes equation in three dimensions are constructed. And commutative diagrams are…

Numerical Analysis · Mathematics 2022-09-01 Xuehai Huang

In this paper we analyze the finite element approximation of the Stokes equations with non-smooth Dirichlet boundary data. To define the discrete solution, we first approximate the boundary datum by a smooth one and then apply a standard…

Numerical Analysis · Mathematics 2019-12-12 Ricardo G. Durán , Lucia Gastaldi , Ariel L. Lombardi

We present a stable finite element method for incompressible nonlinear elasticity based on a four-field mixed formulation involving the displacement, displacement gradient, first Piola--Kirchhoff stress and pressure. Unlike existing…

Numerical Analysis · Mathematics 2026-03-11 Santiago Badia , Wei Li , Ricardo Ruiz-Baier

A new discontinuous Galerkin finite element method for the Stokes equations is developed in the primary velocity-pressure formulation. This method employs discontinuous polynomials for both velocity and pressure on general…

Numerical Analysis · Mathematics 2021-05-05 Xiu Ye , Shangyou Zhang

The Stokes equations play an important role in the incompressible flow simulation. In this paper, a novel divergence-free parametric mixed finite element method is proposed for solving three-dimensional Stokes equations on domains with…

Numerical Analysis · Mathematics 2025-12-19 Lingxiao Li , Haiyan Su , He Zhang , Weiying Zheng

This paper is devoted to the well-posedness analysis of a nonstationary Stokes hemivariational inequality for an incompressible fluid flow described by the Stokes equations subject to a nonsmooth boundary condition of friction type…

Numerical Analysis · Mathematics 2026-03-31 Weimin Han , Shengda Zeng

In this paper, we present a numerical analysis of the hydrostatic Stokes equations, which are linearization of the primitive equations describing the geophysical flows of the ocean and the atmosphere. The hydrostatic Stokes equations can be…

Numerical Analysis · Mathematics 2017-09-05 Tomoya Kemmochi

We introduce a mixed discontinuous/continuous finite element pair for ocean modelling, with continuous quadratic pressure/layer depth and discontinuous velocity. We investigate the finite element pair applied to the linear shallow-water…

Numerical Analysis · Mathematics 2009-11-13 C. J. Cotter , D. A. Ham , C. C. Pain

This paper considers the discretization of the Stokes equations with Scott--Vogelius pairs of finite element spaces on arbitrary shape-regular simplicial grids. A novel way of stabilizing these pairs with respect to the discrete inf-sup…

Numerical Analysis · Mathematics 2022-06-06 Volker John , Xu Li , Christian Merdon , Hongxing Rui