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A note on the space-time variational formulation for the wave equation with source term in
Marco Zank
We derive a variational formulation for the scalar wave equation in the second-order formulation on bounded Lipschitz domains and homogeneous initial conditions. We investigate a v…
A Space-Time Continuous Galerkin Finite Element Method for Linear Schrödinger Equations
Marco Zank
We introduce a space-time finite element method for the linear time-dependent Schrödinger equation with Dirichlet conditions in a bounded Lipschitz domain. The proposed discretizat…
On a modified Hilbert transformation, the discrete inf-sup condition, and error estimates
Richard Löscher, Olaf Steinbach, Marco Zank
In this paper, we analyze the discrete inf-sup condition and related error estimates for a modified Hilbert transformation as used in the space-time discretization of time-dependen…
Wavelet compressed, modified Hilbert transform in the space-time discretization of the heat equation
Helmut Harbrecht, Christoph Schwab, Marco Zank
On a finite time interval , we consider the multiresolution Galerkin discretization of a modified Hilbert transform which arises in the space-time Galerkin di…
Numerical study of conforming space-time methods for Maxwell's equations
Julia I. M. Hauser, Marco Zank
Time-dependent Maxwell's equations govern electromagnetics. Under certain conditions, we can rewrite these equations into a partial differential equation of second order, which in…
Exponential Convergence of -Time-Stepping in Space-Time Discretizations of Parabolic PDEs
Ilaria Perugia, Christoph Schwab, Marco Zank
For linear parabolic initial-boundary value problems with self-adjoint, time-homogeneous elliptic spatial operator in divergence form with Lipschitz-continuous coefficients, and fo…