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
...

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...

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...

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
...

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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