This paper gives an overview of adaptive discretization methods for linear second-order hyperbolic problems such as the acoustic or the elastic wave equation. The emphasis is on Galerkin-type methods for spatial as well as temporal discretization, which also include variants of the Crank-Nicolson and the Newmark finite difference schemes. The adaptive choice of space and time meshes follows the...

We consider stable discretizations in time and space for the linear dynamic consolidation problem describing the wave propagation in a porous solid skeleton which is fully saturated with an incompressible uid. Introducing the hydrostatic pressure, the ow problem is described by Darcy's law. In particular, we discuss the case of nearly impermeable solids which requires inf-sup stable discretizat...

In this paper, we numerically study porosity problems with three different dissipation mechanisms. The root behavior is analyzed for each case. Then, by using the finite element method and Newmark-β scheme, fully discrete approximations are introduced some numerical results described to show energy evolution depending on viscosity coefficient.

In a previous paper [4], we adapted Nitsche’s method for the approximation of the linear elastodynamic unilateral contact problem. The space semi-discrete problem was analyzed and some schemes (θ-scheme, Newmark and a new hybrid scheme) were proposed and proved to be well-posed under appropriate CFL conditons. In the present paper we look at the stability properties of the above-mentioned schem...

This paper gives a review of integration algorithms for finite dimensional mechanical systems that are based on discrete variational principles. The variational technique gives a unified treatment of many symplectic schemes, including those of higher order, as well as a natural treatment of the discrete Noether theorem. The approach also allows us to include forces, dissipation and constraints ...

The paper deals with a numerical analusis for the seismic response of reinforced concrete structures containing cable elements. The cable behaviour is considered as nonconvex and nonmonotone one and is described by generalized subdifferential relations including loosening, elastoplastic fracturing etc. effects. The problem is treated incrementally by double discretization: in space by finite el...