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Optimal convergence of a discontinuous-Galerkin-based immersed boundary method

Adrian J. LewMatteo Negri — 2011

ESAIM: Mathematical Modelling and Numerical Analysis

We prove the optimal convergence of a discontinuous-Galerkin-based immersed boundary method introduced earlier [Lew and Buscaglia, (2008) 427–454]. By switching to a discontinuous Galerkin discretization near the boundary, this method overcomes the suboptimal convergence rate that may arise in immersed boundary methods when strongly imposing essential boundary conditions. We consider a model Poisson's problem with homogeneous boundary conditions over two-dimensional ...

A family of discontinuous Galerkin mixed methods for nearly and perfectly incompressible elasticity

Yongxing ShenAdrian J. Lew — 2012

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

We introduce a family of mixed discontinuous Galerkin (DG) finite element methods for nearly and perfectly incompressible linear elasticity. These mixed methods allow the choice of polynomials of any order  ≥ 1 for the approximation of the displacement field, and of order or  − 1 for the pressure space, and are stable for any positive value of the stabilization parameter. We prove the optimal convergence of the displacement and stress fields in both cases, with error estimates that are independent...

A family of discontinuous Galerkin mixed methods for nearly and perfectly incompressible elasticity

Yongxing ShenAdrian J. Lew — 2012

ESAIM: Mathematical Modelling and Numerical Analysis

We introduce a family of mixed discontinuous Galerkin (DG) finite element methods for nearly and perfectly incompressible linear elasticity. These mixed methods allow the choice of polynomials of any order  ≥ 1 for the approximation of the displacement field, and of order or  − 1 for the pressure space, and are stable for any positive value of the stabilization parameter. We prove the optimal convergence of the displacement and stress fields in...

Optimal convergence of a discontinuous-Galerkin-based immersed boundary method

Adrian J. LewMatteo Negri — 2011

ESAIM: Mathematical Modelling and Numerical Analysis

We prove the optimal convergence of a discontinuous-Galerkin-based immersed boundary method introduced earlier [Lew and Buscaglia, (2008) 427–454]. By switching to a discontinuous Galerkin discretization near the boundary, this method overcomes the suboptimal convergence rate that may arise in immersed boundary methods when strongly imposing essential boundary conditions. We consider a model Poisson's problem with homogeneous boundary conditions over two-dimensional ...

A family of discontinuous Galerkin mixed methods for nearly and perfectly incompressible elasticity

Yongxing ShenAdrian J. Lew — 2012

ESAIM: Mathematical Modelling and Numerical Analysis

We introduce a family of mixed discontinuous Galerkin (DG) finite element methods for nearly and perfectly incompressible linear elasticity. These mixed methods allow the choice of polynomials of any order  ≥ 1 for the approximation of the displacement field, and of order or  − 1 for the pressure space, and are stable for any positive value of the stabilization parameter. We prove the optimal convergence of the displacement and stress fields in...

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