Related papers: Stabilised finite element method for Stokes proble…
This paper proposes a novel way to solve transient linear, and non-linear solid dynamics for compressible, nearly incompressible, and incompressible material in the updated Lagrangian framework for tetrahedral unstructured finite elements.…
In this paper, we first construct a nonconforming finite element pair for the incompressible Stokes problem on quadrilateral grids, and then construct a discrete Stokes complex associated with that finite element pair. The finite element…
This paper aims to improve guaranteed error control for the Stokes problem with a focus on pressure-robustness, i.e. for discretisations that compute a discrete velocity that is independent of the exact pressure. A Prager--Synge type result…
In this paper, we analyze the convergence and optimality of a standard adaptive nonconforming linear element method for the Stokes problem. After establishing a special quasi--orthogonality property for both the velocity and the pressure in…
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…
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…
In this work we study the stability, convergence, and pressure-robustness of discretization methods for incompressible flows with hybrid velocity and pressure. Specifically, focusing on the Stokes problem, we identify a set of assumptions…
We present optimal preconditioners for a recently introduced hybridized discontinuous Galerkin finite element discretization of the Stokes equations. Typical of hybridized discontinuous Galerkin methods, the method has degrees-of-freedom…
The Immersed Boundary method has evolved into one of the most useful computational methods in studying fluid structure interaction. On the other hand, the Immersed Boundary method is also known to suffer from a severe timestep stability…
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier--Stokes equations. A semi-discrete entropy estimate for the entire…
We present and analyze two stabilized finite element methods for solving numerically the Poisson--Nernst--Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for…
We develop a high order cut finite element method for the Stokes problem based on general inf-sup stable finite element spaces. We focus in particular on composite meshes consisting of one mesh that overlaps another. The method is based on…
T. Borrvall and J. Petersson [Topology optimization of fluids in Stokes flow, International Journal for Numerical Methods in Fluids 41 (1) (2003) 77--107] developed the first model for topology optimization of fluids in Stokes flow. They…
We consider linear, hyperbolic systems of balance laws in several space dimensions. They possess non-trivial steady states, which result from the equilibrium between derivatives of the unknowns in different directions, and the sources.…
Application of nonlinearity continuation method to numerical solution of steady-state groundwater flow in variably saturated conditions is presented. In order to solve the system of nonlinear equations obtained by finite volume…
We derive and analyse well-posed boundary conditions for the linear shallow water wave equation. The analysis is based on the energy method and it identifies the number, location and form of the boundary conditions so that the initial…
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…
We consider a surface Stokes problem in stream function formulation on a simply connected oriented surface $\Gamma \subset \mathbb{R}^3$ without boundary. This formulation leads to a coupled system of two second order scalar surface partial…
This article presents stability and convergence analyses of subgrid multiscale stabilized finite element formulation of non-Newtonian power-law fluid flow model strongly coupled with variable coefficients Advection-Diffusion-Reaction…
Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…