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 boundary conditions are imposed using a stabilized Nitsche type approach. Control of the non-physical degrees of freedom, , those outside the physical domain, is obtained thanks to a ghost penalty term for both velocities and pressures. Both inf-sup stable and stabilized velocity pressure pairs are considered....
We propose a discontinuous Galerkin method for linear elasticity, based on discontinuous piecewise linear approximation of the displacements. We show optimal order a priori error estimates, uniform in the incompressible limit, and thus locking is avoided. The discontinuous Galerkin method is closely related to the non-conforming Crouzeix–Raviart (CR) element, which in fact is obtained when one of the stabilizing parameters tends to infinity. In the case of the elasticity operator, for which the...
In this note, we propose and analyse a method for handling interfaces between non-matching grids based on an approach suggested by Nitsche (1971) for the approximation of Dirichlet boundary conditions. The exposition is limited to self-adjoint elliptic problems, using Poisson’s equation as a model. A priori and a posteriori error estimates are given. Some numerical results are included.
In this note, we propose and analyse a method for handling
interfaces between non-matching grids based on an approach
suggested by Nitsche (1971) for the approximation of
Dirichlet boundary conditions. The exposition is limited to
self-adjoint elliptic problems, using Poisson's equation as a
model. and error estimates are given. Some
numerical results are included.
We propose a discontinuous Galerkin method for linear
elasticity, based on discontinuous piecewise linear approximation
of the displacements. We show optimal order error estimates,
uniform in the incompressible limit, and thus locking is avoided.
The discontinuous Galerkin method is closely related to the
non-conforming Crouzeix–Raviart (CR) element, which in fact is
obtained when one of the stabilizing parameters tends to infinity.
In the case of the elasticity operator, for which the...
In this paper we propose a finite element method for the approximation of second order elliptic problems on composite grids. The method is based on continuous piecewise polynomial approximation on each grid and weak enforcement of the proper continuity at an artificial interface defined by edges (or faces) of one the grids. We prove optimal order a priori and energy type a posteriori error estimates in 2 and 3 space dimensions, and present some numerical examples.
In this paper we propose a finite element method for the approximation of
second order elliptic problems on composite grids. The method is
based on continuous piecewise polynomial approximation on each
grid and weak enforcement of the proper continuity at an
artificial interface defined by edges (or faces) of one the grids.
We prove optimal order and energy type error estimates in 2 and 3 space dimensions,
and present some numerical examples.
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