In Chapter 1 we presented basic ideas for the reduction of boundary value problems of the
Laplacian to various forms of boundary integral equations based on the direct approach …

We propose and analyse new space-time Galerkin-Bubnov-type finite element formulations
of parabolic and hyperbolic second-order partial differential equations in finite time intervals …

We present a space–time Trefftz discontinuous Galerkin method for approximating the
acoustic wave equation semi-explicitly on tent pitched meshes. DG Trefftz methods use …

We present a space–time ultra-weak discontinuous Galerkin discretization of the linear
Schrödinger equation with variable potential. The proposed method is well-posed and quasi …

In this paper, we consider a variational formulation for the Dirichlet problem of the wave
equation with zero boundary and initial conditions, where we use integration by parts in …

Trefftz schemes are high-order Galerkin methods whose discrete spaces are made of
elementwise exact solutions of the underlying partial differential equation (PDE). Trefftz …

The purpose of this note… is to sort out my own thoughts… and to solicit ideas from others.
Lloyd N. Trefethen Three mysteries of Gaussian elimination Since 2008, when the first …

We study space–time isogeometric discretizations of the linear acoustic wave equation that
use splines of arbitrary degree p, both in space and time. We propose a space–time …

A space-time Trefftz discontinuous Galerkin method for the Schrödinger equation with
piecewise-constant potential is proposed and analyzed. Following the spirit of Trefftz …

Abstract In Trefftz discontinuous Galerkin methods a partial differential equation is
discretized using discontinuous shape functions that are chosen to be elementwise in the …