1,188 research outputs found
A Stabilized Cut Streamline Diffusion Finite Element Method for Convection-Diffusion Problems on Surfaces
We develop a stabilized cut finite element method for the stationary convection diffusion problem
on a surface embedded in R
d
. The cut finite element method is based on using an embedding of the
surface into a three dimensional mesh consisting of tetrahedra and then using the restriction of the
standard piecewise linear continuous elements to a piecewise linear approximation of the surface.
The stabilization consists of a standard streamline diffusion stabilization term on the discrete
surface and a so called normal gradient stabilization term on the full tetrahedral elements in the
active mesh. We prove optimal order a priori error estimates in the standard norm associated with
the streamline diffusion method and bounds for the condition number of the resulting stiffness
matrix. The condition number is of optimal order for a specific choice of method parameters.
Numerical examples supporting our theoretical results are also included
A cut finite element method for coupled bulk-surface problems on time-dependent domains
In this contribution we present a new computational method for coupled
bulk-surface problems on time-dependent domains. The method is based on a
space-time formulation using discontinuous piecewise linear elements in time
and continuous piecewise linear elements in space on a fixed background mesh.
The domain is represented using a piecewise linear level set function on the
background mesh and a cut finite element method is used to discretize the bulk
and surface problems. In the cut finite element method the bilinear forms
associated with the weak formulation of the problem are directly evaluated on
the bulk domain and the surface defined by the level set, essentially using the
restrictions of the piecewise linear functions to the computational domain. In
addition a stabilization term is added to stabilize convection as well as the
resulting algebraic system that is solved in each time step. We show in
numerical examples that the resulting method is accurate and stable and results
in well conditioned algebraic systems independent of the position of the
interface relative to the background mesh
A finite element method for solving the incompressible Navier-Stokes equations at low and high Reynolds numbers using finite calculus. Application to fluid-structure interaction
The main objective of this monograph is to develop a stabilized finite element
method (FEM) for solving the incompressible Navier-Stokes equations. Using Finite Calculus (FIC),
which is a methodology developed by E. On˜ate and co-workers at CIMNE (International Center for
Numerical Methods in Engineering), flows with a wide range of Reynolds numbers can be modeled. The
secondary objective is to test the applicability of the FIC/FEM model to fluid-structure
interaction (FSI) emphasizing aero-elasticity. The implementation of the model is carried out
within KRATOS, a finite element code for solving multi-physics problems developed at
CIMNE
Finite elements for scalar convection-dominated equations and incompressible flow problems - A never ending story?
The contents of this paper is twofold. First, important recent results concerning finite element
methods for convection-dominated problems and incompressible flow problems are described that
illustrate the activities in these topics. Second, a number of, in our opinion, important problems in
these fields are discussed
Meshless analysis of incompressible flows using the Finite Point Method
A stabilized finite point method (FPM) for the meshless analysis of incompressible fluid flow problems is presented. The stabilization approach is based in the finite calculus (FIC) procedure. An enhanced fractional step procedure allowing the semi-implicit numerical solution of incompressible fluids using the FPM is described. Examples of application of the stabilized FPM to the solution of incompressible flow problems are presented
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