Fictitious domain methods using cut elements: III. A stabilized Nitsche method for Stokes’ problem
Erik Burman,Peter Hansbo +1 more
Reads0
Chats0
TLDR
In this paper, the authors extend their results on fictitious domain methods for Poisson's problem to the case of incompressible elasticity, or Stokes' problem, where the mesh is not fitted to the domain boundary.Abstract:
We extend our results on fictitious domain methods for Poisson’s problem to the case of incompressible elasticity, or Stokes’ problem. The mesh is not fitted to the domain boundary. Instead boundar ...read more
Citations
More filters
Journal ArticleDOI
CutFEM: Discretizing geometry and partial differential equations
TL;DR: Recent advances on robust unfitted finite element methods on cut meshes designed to facilitate computations on complex geometries obtained from computer‐aided design or image data from applied sciences are discussed and illustrated numerically.
Journal ArticleDOI
A cut finite element method for a Stokes interface problem
TL;DR: A Nitsche formulation is proposed which allows for discontinuities along the interface with optimal a priori error estimates in the Stokes equations involving two immiscible incompressible fluids with different viscosities and with surface tension.
Journal ArticleDOI
A Stabilized Nitsche Fictitious Domain Method for the Stokes Problem
TL;DR: In this paper, a finite element method for the Stokes problem on fictitious domains is presented, which is based on a stabilized Nitsche method with ghost penalties for the velocity and pressure.
Journal ArticleDOI
An unfitted Nitsche method for incompressible fluid–structure interaction using overlapping meshes
TL;DR: A stability analysis for the space semi-discretized problem is given and it is shown how this estimate may be used to derive optimal error estimates for smooth solutions, irrespectively of the mesh/interface intersection.
Journal ArticleDOI
The shifted boundary method for embedded domain computations. Part I: Poisson and Stokes problems
Alex Main,Guglielmo Scovazzi +1 more
TL;DR: A new finite element method for embedded domain computations, which falls in the category of surrogate/approximate boundary algorithms, is proposed, which is simple, efficient, and also robust, since it is not affected by the small-cut-cell problem.
References
More filters
Journal ArticleDOI
Mathematical Analysis and Numerical Methods for Science and Technology
TL;DR: These six volumes as mentioned in this paper compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers.
Journal ArticleDOI
Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind
Journal ArticleDOI
A stable finite element for the stokes equations
TL;DR: In this paper, a new velocity-pressure finite element for the computation of Stokes flow is presented, which satisfies the usual inf-sup condition and converges with first order for both velocities and pressure.
Journal ArticleDOI
An unfitted finite element method, based on Nitsche's method, for elliptic interface problems
Anita Hansbo,Peter Hansbo +1 more
TL;DR: The method allows for discontinuities, internal to the elements, in the approximation across the interface, and it is shown that optimal order of convergence holds without restrictions on the location of the interface relative to the mesh.
Journal ArticleDOI
Fictitious domain finite element methods using cut elements
Erik Burman,Peter Hansbo +1 more
TL;DR: In this paper, the classical Nitsche type weak boundary conditions are extended to a fictitious domain setting and an additional penalty term, acting on the jumps of the gradients over element faces in the interface zone, is added to ensure that the conditioning of the matrix is independent of how the boundary cuts the mesh.
Related Papers (5)
An unfitted finite element method, based on Nitsche's method, for elliptic interface problems
Anita Hansbo,Peter Hansbo +1 more