Related papers: A discontinuous Galerkin coupling for nonlinear el…
We consider a nonlocal linear elastic wave model. We approximate the model using a spectral Galerkin method in space and analyze error in such an approximation. We perform some numerical experiments to demonstrate the scheme.
We present a novel approach for simulating acoustic (pressure) wave propagation across different media separated by a diffuse interface through the use of a weak compressibility formulation. Our method builds on our previous work on an…
We analyze a discontinuous Galerkin FEM-BEM scheme for a second order elliptic transmission problem posed in the three-dimensional space. The symmetric variational formulation is discretized by nonconforming Raviart-Thomas finite elements…
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by…
A discontinuous Galerkin method for approximating the Vlasov-Poisson system of equations describing the time evolution of a collisionless plasma is proposed. The method is mass conservative and, in the case that piecewise constant functions…
In this article, interior penalty discontinuous Galerkin methods using immersed finite element functions are employed to solve parabolic interface problems. Typical semi-discrete and fully discrete schemes are presented and analyzed.…
This paper presents a multiscale Petrov-Galerkin finite element method for time-harmonic acoustic scattering problems with heterogeneous coefficients in the high-frequency regime. We show that the method is pollution- free also in the case…
A nonsymmetric discontinuous Galerkin FEM with interior penalties has been applied to one-dimensional singularly perturbed reaction-diffusion problems. Using higher order splines on Shishkin-type layer-adapted meshes and certain graded…
We study a class of models for nonlinear acoustics, including the well-known Westervelt and Kuznetsov equations, as well as a model of Rasmussen that can be seen as a thermodynamically consistent modification of the latter. Using…
We give an a priori analysis of a semi-discrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics which involves an energy density depending not only on the strain but also the strain gradient. A…
A mathematical model for an elastoplastic continuum subject to large strains is presented. The inelastic response is modeled within the frame of rate-dependent gradient plasticity for nonsimple materials. Heat diffuses through the continuum…
We extend the finite element method introduced by Lakkis and Pryer [2011] to approximate the solution of second order elliptic problems in nonvariational form to incorporate the discontinuous Galerkin (DG) framework. This is done by viewing…
We consider a (possibly) nonlinear interface problem in 2D and 3D, which is solved by use of various adaptive FEM-BEM coupling strategies, namely the Johnson-N\'ed\'elec coupling, the Bielak-MacCamy coupling, and Costabel's symmetric…
In this paper, we study the numerical approximation of a coupled system of elliptic-parabolic equations posed on two separated spatial scales. The model equations describe the interplay between macroscopic and microscopic pressures in an…
A Galerkin finite element method for the membrane elasticity problem on a meshed surface is constructed by using two-dimensional elements extended into three dimensions. The membrane finite element model is established using the intrinsic…
A symmetric boundary integral formulation for the transient scattering of acoustic waves off homogeneous and isotropic elastic obstacles is analyzed. Both the acoustic scattered field and the elastodynamic excited field are represented…
We consider in this paper a velocity discretized version of the full linear kinetic BGK model and the corresponding limit for small Knudsen number, the linearised Euler or acoustic system. Considering these equations on networks, coupling…
We introduce and analyze a discontinuous Galerkin FEM/BEM method for a time-harmonic eddy current problem written in terms of the magnetic field. We use nonconforming N\'ed\'elec finite elements on a partition of the interior domain coupled…
We consider spectral mixed discontinuous Galerkin finite element discretizations of the Lam\'e system of linear elasticity in polyhedral domains in $\mathbb{R}^3$. In order to resolve possible corner, edge, and corner-edge singularities,…
We solve acoustic scattering problems by means of the isogeometric boundary integral equation method. In order to avoid spurious modes, we apply the combined field integral equations for either sound-hard scatterers or sound-soft…