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A finite element convergence analysis for 3D Stokes equations in case of variational crimes

Petr Knobloch (2000)

Applications of Mathematics

We investigate a finite element discretization of the Stokes equations with nonstandard boundary conditions, defined in a bounded three-dimensional domain with a curved, piecewise smooth boundary. For tetrahedral triangulations of this domain we prove, under general assumptions on the discrete problem and without any additional regularity assumptions on the weak solution, that the discrete solutions converge to the weak solution. Examples of appropriate finite element spaces are given.

A finite element discretization of the contact between two membranes

Faker Ben Belgacem, Christine Bernardi, Adel Blouza, Martin Vohralík (2009)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

From the fundamental laws of elasticity, we write a model for the contact between two membranes and we perform the analysis of the corresponding system of variational inequalities. We propose a finite element discretization of this problem and prove its well-posedness. We also establish a priori and a posteriori error estimates.

A finite element discretization of the contact between two membranes

Faker Ben Belgacem, Christine Bernardi, Adel Blouza, Martin Vohralík (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

From the fundamental laws of elasticity, we write a model for the contact between two membranes and we perform the analysis of the corresponding system of variational inequalities. We propose a finite element discretization of this problem and prove its well-posedness. We also establish a priori and a posteriori error estimates.

A finite element discretization of the three-dimensional Navier–Stokes equations with mixed boundary conditions

Christine Bernardi, Frédéric Hecht, Rüdiger Verfürth (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a variational formulation of the three-dimensional Navier–Stokes equations with mixed boundary conditions and prove that the variational problem admits a solution provided that the domain satisfies a suitable regularity assumption. Next, we propose a finite element discretization relying on the Galerkin method and establish a priori and a posteriori error estimates.

A finite element method for domain decomposition with non-matching grids

Roland Becker, Peter Hansbo, Rolf Stenberg (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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.

A finite element method for domain decomposition with non-matching grids

Roland Becker, Peter Hansbo, Rolf Stenberg (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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.

A finite element method for stiffened plates

Ricardo Durán, Rodolfo Rodríguez, Frank Sanhueza (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The aim of this paper is to analyze a low order finite element method for a stiffened plate. The plate is modeled by Reissner-Mindlin equations and the stiffener by Timoshenko beams equations. The resulting problem is shown to be well posed. In the case of concentric stiffeners it decouples into two problems, one for the in-plane plate deformation and the other for the bending of the plate. The analysis and discretization of the first one is straightforward. The second one is shown to have a solution...

A finite element method for stiffened plates

Ricardo Durán, Rodolfo Rodríguez, Frank Sanhueza (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

The aim of this paper is to analyze a low order finite element method for a stiffened plate. The plate is modeled by Reissner-Mindlin equations and the stiffener by Timoshenko beams equations. The resulting problem is shown to be well posed. In the case of concentric stiffeners it decouples into two problems, one for the in-plane plate deformation and the other for the bending of the plate. The analysis and discretization of the first one is straightforward. The second one is shown to have a solution...

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