34 citations · 67 across the 16 of their papers we have counts for
16 papers
Comparing domain decomposition preconditioners for non-conforming Helmholtz discretizations
Moritz Gallauner, Emile Parolin, Paul Stocker +1
We compare additive and multiplicative domain decomposition preconditioners, without coarse correction, for three non-conforming polynomial discretizations of Helmholtz problems: d…
Embedded Trefftz DG method for steady Navier-Stokes flow. Part I: Oseen linearization
Paul Stocker, Igor Voulis, Christoph Lehrenfeld +1
We develop an embedded Trefftz-DG method for the Oseen problem and prove a complete stability and quasi-optimality theory in standard DG norms. The key ingredient is a construction…
Embedded Trefftz DG method for steady Navier-Stokes flow. Part II: Nonlinear problem
Paul Stocker, Igor Voulis, Christoph Lehrenfeld +1
We develop and analyze an embedded Trefftz-DG method for the steady incompressible Navier-Stokes equations, based on the reduced Oseen discretization from Part I. The main difficul…
Embedded Trefftz DG method for reaction-diffusion problems on anisotropic meshes
Sergio Gómez, Chiara Perinati, Paul Stocker +1
We present and analyze an embedded Trefftz discontinuous Galerkin method for reaction-diffusion problems on anisotropic meshes. The method is constructed by imposing a relaxed loca…
A discontinuous Galerkin method for elliptic-hyperbolic equations: the Tricomi problem
Chiara Perinati, Lise-Marie Imbert-Gérard, Andrea Moiola +1
We present and analyze a discontinuous Galerkin method for the numerical solution of a class of second-order linear mixed-type partial differential equations, i.e. equations that c…
Embedded Trefftz DG framework for the analysis of discretizations with local-global decompositions
Philip L. Lederer, Christoph Lehrenfeld, Paul Stocker +1
This paper presents a framework for the analysis of discretization methods based on the decomposition into local and global problems. We apply the framework to provide a comprehens…
Sparsity comparison of polytopal finite element methods
Christoph Lehrenfeld, Paul Stocker, Maximilian Zienecker
In this work we compare crucial parameters for efficiency of different finite element methods for solving partial differential equations (PDEs) on polytopal meshes. We consider the…
Trefftz Discontinuous Galerkin discretization for the Stokes problem
Philip L. Lederer, Christoph Lehrenfeld, Paul Stocker
We introduce a new discretization based on the Trefftz-DG method for solving the Stokes equations. Discrete solutions of a corresponding method fulfill the Stokes equation pointwis…
On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation
Sergio Gómez, Andrea Moiola, Ilaria Perugia +1
We study the approximation properties of complex-valued polynomial Trefftz spaces for the -dimensional linear time-dependent Schrödinger equation. More precisely, we prove t…
Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems
Fabian Heimann, Christoph Lehrenfeld, Paul Stocker +1
We propose a new geometrically unfitted finite element method based on discontinuous Trefftz ansatz spaces. Trefftz methods allow for a reduction in the number of degrees of freedo…
A new T-compatibility condition and its application to the discretization of the damped time-harmonic Galbrun's equation
Martin Halla, Christoph Lehrenfeld, Paul Stocker
We consider the approximation of weakly T-coercive operators. The main property to ensure the convergence thereof is the regularity of the approximation (in the vocabulary of discr…
Robust finite element discretizations for a simplified Galbrun's equation
Tilman Alemán, Martin Halla, Christoph Lehrenfeld +1
Driven by the challenging task of finding robust discretization methods for Galbrun's equation, we investigate conditions for stability and different aspects of robustness for diff…
Embedded Trefftz discontinuous Galerkin methods
Christoph Lehrenfeld, Paul Stocker
In Trefftz discontinuous Galerkin methods a partial differential equation is discretized using discontinuous shape functions that are chosen to be elementwise in the kernel of the…
A space-time quasi-Trefftz DG method for the wave equation with piecewise-smooth coefficients
Lise-Marie Imbert-Gérard, Andrea Moiola, Paul Stocker
Trefftz methods are high-order Galerkin schemes in which all discrete functions are elementwise solution of the PDE to be approximated. They are viable only when the PDE is linear…
An entropy structure preserving space-time formulation for cross-diffusion systems: Analysis and Galerkin discretization
Marcel Braukhoff, Ilaria Perugia, Paul Stocker
Cross-diffusion systems are systems of nonlinear parabolic partial differential equations that are used to describe dynamical processes in several application, including chemical c…
Tent pitching and Trefftz-DG method for the acoustic wave equation
Ilaria Perugia, Joachim Schöberl, Paul Stocker +1
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 discontinu…