This chapter presents an introduction to multiscale and stabilized methods, which represent
unified approaches to modeling and numerical solution of fluid dynamic phenomena. Finite …

We propose a new approach for the stabilization of linear tetrahedral finite elements in the
case of nearly incompressible transient solid dynamics computations. Our method is based …

We propose a new computational approach for embedded boundary simulations of
hyperbolic systems and, in particular, the linear wave equations and the nonlinear shallow …

A new nodal mixed finite element is proposed for the simulation of linear elastodynamics
and wave propagation problems in time domain. Our method is based on equal-order …

In most classical approaches of computational geophysics for seismic wave propagation
problems, complex surface topography is either accounted for by boundary-fitted …

We propose a new Nitsche-type approach for weak enforcement of normal velocity
boundary conditions for a Lagrangian discretization of the compressible shock …

In this paper we propose a new high order accurate space–time discontinuous Galerkin
(DG) finite element scheme for the solution of the linear elastic wave equations in first order …

We consider fully discrete embedded finite element approximations for a shallow water
hyperbolic problem and its reduced-order model. Our approach is based on a fixed …

In the discontinuous Galerkin framework, a generalized anisotropic wave impedance is
proposed, to succinctly solve the Riemann problem for 3-D full-anisotropic poroelastic …

We present a monolithic arbitrary Lagrangian–Eulerian (ALE) finite element method for
computing highly transient flows with strong shocks. We use a variational multiscale (VMS) …