BR2 discontinuous Galerkin methods for finite hyperelastic deformations

Hybrid High-Order methods for finite deformations of hyperelastic materials

We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order k ≥ 1 on the mesh skeleton, together with cell-based polynomials that can be eliminated locally by static condensation. The discrete problem is written as the minimization of the broken nonlinear ela...

Parallel Iterative Discontinuous Galerkin Finite-element Methods

We compare an iterative asynchronous parallel algorithm for the solution of partial diierential equations, with a synchronous algorithm , in terms of termination detection schemes and performance. Both algorithms are based on discontinuous Galerkin nite-element methods, in which the local elements provide a natural decomposition of the problem into computationally-independent sets. We demonstra...

Discontinuous Galerkin Finite Element Methods for Photonic Crystals

Krylov-Subspace Preconditioners for Discontinuous Galerkin Finite Element Methods

Standard (conforming) finite element approximations of convection-dominated convectiondiffusion problems often exhibit poor stability properties that manifest themselves as nonphysical oscillations polluting the numerical solution. Various techniques have been proposed for the stabilisation of finite element methods (FEMs) for convection-diffusion problems, such as the popular streamline upwind...

Discontinuous Galerkin finite element methods for second order hyperbolic problems

In this paper, we prove a priori and a posteriori error estimates for a finite element method for linear second order hyperbolic problems (linear wave equations) based on using spacetime finite element discretizations (for displacements and displacement velocities) with (bilinear) basis functions which are continuous in space and discontinuous in time. We refer to methods of this form as discon...