Mathematicsisplayinganevermoreimportant…-ical sciences, provoking a blurring of
boundaries between scienti? c disciplines and a resurgence of interest in the modern as …

In this paper, we present several extensions of theoretical tools for the analysis of
discontinuous Galerkin (DG) method beyond the linear case. We define broken Sobolev …

In this work we propose and analyze a novel Hybrid High-Order discretization of a class of
(linear and) nonlinear elasticity models in the small deformation regime which are of …

We develop a family of new interior penalty discontinuous Galerkin methods for the Keller–
Segel chemotaxis model. This model is described by a system of two nonlinear PDEs: a …

We propose a high-order discontinuous Galerkin scheme for nonlinear acoustic waves on
polytopic meshes. To model sound propagation with losses through homogeneous media …

This manuscript deals with the hp error analysis of a hybrid discontinuous Galerkin method
for incompressible flow. Besides the usual coercivity and boundedness estimates, we …

We consider semi-discrete discontinuous Galerkin approximations of both displacement and
displacement-stress formulations of the elastodynamics problem. We prove the stability …

In this paper we study space discretizations of a general class of first-and second-order
quasilinear wave-type problems. We present a rigorous error analysis based on a …

We study the spatial discretization of Westervelt's quasi-linear strongly damped wave
equation by piecewise linear finite elements. Our approach employs the Banach fixed-point …

In this paper, we consider the symmetric interior penalty discontinuous Galerkin (SIPG)
method with piecewise polynomials of degree r≥ 1 for a class of quasi-linear elliptic …