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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

This article reports on the confluence of two streams of research, one emanating from the fields of numerical analysis and scientific computation, the other from topology and geometry. In it we consider the numerical discretization of…

Numerical Analysis · Mathematics 2014-01-29 Douglas N. Arnold , Richard S. Falk , Ragnar Winther

In recent years a great deal of attention has been paid to discretizations of the incompressible Stokes equations that exactly preserve the incompressibility constraint. These are of substantial interest because these discretizations are…

Numerical Analysis · Mathematics 2024-03-18 Patrick E. Farrell , Lawrence Mitchell , L. Ridgway Scott

A dynamic linear thermo-poroelasticity model, containing inertial and relaxation terms with second-order time derivatives, is investigated in this paper. The mathematical and numerical analysis of this model is performed in the frequency…

Numerical Analysis · Mathematics 2025-11-25 Hongpeng Li , Cristian Carcamo , Hongxing Rui , Volker John

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

We consider a scalar diffusion equation with a sign-changing coefficient in its principle part. The well-posedness of such problems has already been studied extensively provided that the contrast of the coefficient is non-critical.…

Numerical Analysis · Mathematics 2025-04-11 Martin Halla , Florian Oberender

Numerical analysis for the stochastic Stokes equations is still challenging even though it has been well done for the corresponding deterministic equations. In particular, the pre-existing error estimates of finite element methods for the…

Numerical Analysis · Mathematics 2023-12-13 Buyang Li , Shu Ma , Weiwei Sun

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

Local behaviors near boundary are analyzed for solutions of the Stokes and Navier-Stoke equations in the half space with localized non-smooth boundary data. We construct solutions of Stokes equations whose velocity field is not bounded near…

Analysis of PDEs · Mathematics 2024-06-07 TongKeun Chang , Kyungkeun Kang

We present a finite element approach for diffusion problems with thermal fluctuations based on a fluctuating hydrodynamics model. The governing transport equations are stochastic partial differential equations with a fluctuating forcing…

Numerical Analysis · Mathematics 2024-03-21 P. Martínez-Lera , M. De Corato

We consider flux-corrected finite element discretizations of 3D convection-dominated transport problems and assess the computational efficiency of algorithms based on such approximations. The methods under investigation include…

Numerical Analysis · Mathematics 2024-01-15 Abhinav Jha , Ondřej Pártl , Naveed Ahmed , Dmitri Kuzmin

We present a parametric finite element approximation of two-phase flow. This free boundary problem is given by the Stokes equations in the two phases, which are coupled via jump conditions across the interface. Using a novel variational…

Numerical Analysis · Mathematics 2015-06-02 John W. Barrett , Harald Garcke , Robert Nürnberg

We investigate the existence of weak solutions to a certain system of partial differential equations, modelling the behaviour of a compressible non-Newtonian fluid for small Reynolds number. We construct the weak solutions despite the lack…

Analysis of PDEs · Mathematics 2023-05-24 Milan Pokorný , Maja Szlenk

We study the weak Galerkin finite element method for Stokes problem. A new weak Galerkin finite element velocity-pressure space pair is presented which satisfies the discrete inf-sup condition. Based on this space pair, we establish a…

Numerical Analysis · Mathematics 2018-01-30 Tie Zhang , Tao Lin

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

In this paper, we consider the Stokes problem with Dirichlet boundary conditions and the constant kinematic viscosity $\nu$ in an axis-aligned domain $\Omega$. We decouple the velocity $\bm u$ and pressure $p$ by deriving a novel biharmonic…

Numerical Analysis · Mathematics 2025-06-17 Qiwei Feng , Bin Han , Michael Neilan

In this paper, we develop a patch reconstruction finite element method for the Stokes problem. The weak formulation of the interior penalty discontinuous Galerkin is employed. The proposed method has a great flexibility in velocity-pressure…

Numerical Analysis · Mathematics 2019-10-01 Ruo Li , Zhiyuan Sun , Fanyi Yang , Zhijian Yang

In the present article, we introduce and study a model addressing the Stokes problem with non-linear boundary conditions of the Tresca type. We suggest a new procedure for regularizing incompressible fluid, i.e. we assume that the…

Analysis of PDEs · Mathematics 2025-03-04 A. Zafrar

We propose a new least squares finite element method to solve the Stokes problem with two sequential steps. The approximation spaces are constructed by patch reconstruction with one unknown per element. For the first step, we reconstruct an…

Numerical Analysis · Mathematics 2020-03-05 Ruo Li , Fanyi Yang

The aim of this work is to analyze the finite element approximation of the two-dimensional stationary Navier-Stokes equations with non-smooth Dirichlet boundary data. The discrete approximation is obtained by considering the Navier-Stokes…

Numerical Analysis · Mathematics 2026-02-09 María Gabriela Armentano , Mauricio Mendiluce