6 papers
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…
Towards coercive boundary element methods for the wave equation
Olaf Steinbach, Carolina Urzúa-Torres, Marco Zank
In this note, we discuss the ellipticity of the single layer boundary integral operator for the wave equation in one space dimension. This result not only generalizes the well-know…
Numerical results for an unconditionally stable space-time finite element method for the wave equation
Richard Löscher, Olaf Steinbach, Marco Zank
In this work, we introduce a new space-time variational formulation of the second-order wave equation, where integration by parts is also applied with respect to the time variable,…
Higher-Order Space-Time Continuous Galerkin Methods for the Wave Equation
Marco Zank
We consider a space-time variational formulation of the second-order wave equation, where integration by parts is also applied with respect to the time variable. Conforming tensor-…
A generalized inf-sup stable variational formulation for the wave equation
Olaf Steinbach, Marco Zank
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…
Efficient Direct Space-Time Finite Element Solvers for Parabolic Initial-Boundary Value Problems in Anisotropic Sobolev Spaces
Ulrich Langer, Marco Zank
We consider a space-time variational formulation of parabolic initial-boundary value problems in anisotropic Sobolev spaces in combination with a Hilbert-type transformation. This…