Paul Stocker
YOU?
Author Swipe
View article: Inf-sup stable space–time Local Discontinuous Galerkin method for the heat equation
Inf-sup stable space–time Local Discontinuous Galerkin method for the heat equation Open
We propose and analyze a space–time Local Discontinuous Galerkin method for the approximation of the solution to parabolic problems. The method allows for very general discrete spaces and prismatic space–time meshes. Existence and uniquene…
View article: A new T-compatibility condition and its application to the discretization of the damped time-harmonic Galbrun’s equation
A new T-compatibility condition and its application to the discretization of the damped time-harmonic Galbrun’s equation Open
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 discrete approximation schemes). In a previous work the existenc…
View article: Embedded Trefftz DG framework for the analysis of discretizations with local-global decompositions
Embedded Trefftz DG framework for the analysis of discretizations with local-global decompositions Open
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 comprehensive error analysis for the embedded Trefftz discontinuous G…
View article: Inf-sup stable space-time Local Discontinuous Galerkin method for the heat equation
Inf-sup stable space-time Local Discontinuous Galerkin method for the heat equation Open
We propose and analyze a space-time Local Discontinuous Galerkin method for the approximation of the solution to parabolic problems. The method allows for very general discrete spaces and prismatic space-time meshes. Existence and uniquene…
View article: Sparsity comparison of polytopal finite element methods
Sparsity comparison of polytopal finite element methods Open
In this work we compare crucial parameters for efficiency of different finite element methods for solving partial differential equations on polytopal meshes. We consider the virtual element method (VEM) and different discontinuous Galerkin…
View article: Polynomial quasi-Trefftz DG for PDEs with smooth coefficients: elliptic problems
Polynomial quasi-Trefftz DG for PDEs with smooth coefficients: elliptic problems Open
Trefftz schemes are high-order Galerkin methods whose discrete spaces are made of elementwise exact solutions of the underlying PDE. Trefftz basis functions can be easily computed for many PDEs that are linear, homogeneous, and have piecew…
View article: Sparsity comparison of polytopal finite element methods
Sparsity comparison of polytopal finite element methods Open
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 Virtual Element Method (VEM) and different Discontinuous G…
View article: Trefftz discontinuous Galerkin discretization for the Stokes problem
Trefftz discontinuous Galerkin discretization for the Stokes problem Open
We introduce a new discretization based on a polynomial Trefftz-DG method for solving the Stokes equations. Discrete solutions of this method fulfill the Stokes equations pointwise within each element and yield element-wise divergence-free…
View article: On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation
On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation Open
We study the approximation properties of complex-valued polynomial Trefftz spaces for the (d+1)-dimensional linear time-dependent Schrödinger equation. More precisely, we prove that for the space–time Trefftz discontinuous Galerkin variati…
View article: Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems
Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems Open
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 freedom in discontinuous Galerkin methods, thereby, the costs for…
View article: Trefftz Discontinuous Galerkin discretization for the Stokes problem
Trefftz Discontinuous Galerkin discretization for the Stokes problem Open
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 pointwise within each element and yield element-wise divergence-fre…
View article: On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation
On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation Open
We study the approximation properties of complex-valued polynomial Trefftz spaces for the $(d+1)$-dimensional linear time-dependent Schrödinger equation. More precisely, we prove that for the space-time Trefftz discontinuous Galerkin varia…
View article: Embedded Trefftz discontinuous Galerkin methods
Embedded Trefftz discontinuous Galerkin methods Open
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 corresponding differential operator. We propose a new varia…
View article: Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems
Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems Open
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 freedom in discontinuous Galerkin methods, thereby, the costs for…
View article: A space–time quasi-Trefftz DG method for the wave equation with piecewise-smooth coefficients
A space–time quasi-Trefftz DG method for the wave equation with piecewise-smooth coefficients Open
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 and its coefficients are piecewise-constant. We introduce a…
View article: A new T-compatibility condition and its application to the discretization of the damped time-harmonic Galbrun's equation
A new T-compatibility condition and its application to the discretization of the damped time-harmonic Galbrun's equation Open
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 discrete approximation schemes). In a previous work the existenc…
View article: Robust finite element discretizations for a simplified Galbrun's equation
Robust finite element discretizations for a simplified Galbrun's equation Open
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 different finite element schemes on a simplified version of the…
View article: NGSTrefftz: Add-on to NGSolve for Trefftzmethods
NGSTrefftz: Add-on to NGSolve for Trefftzmethods Open
NGSTrefftz is an add-on to Netgen/NGSolve, a finite element software for the numerical treatment of partial differential equations (PDEs).The package implements Trefftz based discontinuous Galerkin (DG) methods in NGSolve.Trefftz methods r…
View article: An Entropy Structure Preserving Space-Time Formulation for Cross-Diffusion Systems: Analysis and Galerkin Discretization
An Entropy Structure Preserving Space-Time Formulation for Cross-Diffusion Systems: Analysis and Galerkin Discretization Open
Cross-diffusion systems are systems of nonlinear parabolic partial\ndifferential equations that are used to describe dynamical processes in several\napplication, including chemical concentrations and cell biology. We present a\nspace-time …
View article: Embedded Trefftz discontinuous Galerkin methods
Embedded Trefftz discontinuous Galerkin methods Open
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 corresponding differential operator. We propose a new varia…
View article: Numerical treatment of the vectorial equations of solar oscillations
Numerical treatment of the vectorial equations of solar oscillations Open
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 different finite element schemes on a simplified version of the…
View article: A space-time quasi-Trefftz DG method for the wave equation with piecewise-smooth coefficients
A space-time quasi-Trefftz DG method for the wave equation with piecewise-smooth coefficients Open
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 and its coefficients are piecewise constant. We introduce a…
View article: An entropy structure preserving space-time Galerkin method for cross-diffusion systems
An entropy structure preserving space-time Galerkin method for cross-diffusion systems Open
Cross-diffusion systems are systems of nonlinear parabolic partial differential equations that are used to describe dynamical processes in several application, including chemical concentrations and cell biology. We present a space-time app…
View article: Tent pitching and Trefftz-DG method for the acoustic wave equation
Tent pitching and Trefftz-DG method for the acoustic wave equation Open
View article: Brexit and the mainstreaming of the British far right
Brexit and the mainstreaming of the British far right Open
In an extract from his new book English Uprising: Brexit and the Mainstreaming of the Far Right, Paul Stocker (Teesside University) looks at the role Vote Leave's inaccurate claim that Turkey was about to join the EU, and its 'Breaking Poi…
View article: Plane wave-based approximation methods for the Helmholtz equation
Plane wave-based approximation methods for the Helmholtz equation Open
Ebene Wellen lösen die homogene Helmholtz-Gleichung (lokal) und bieten daher eine gängige Wahl als Testfunktionen in Finite-Elemente-Methoden für die Helmholtz-Gleichung. Die Arbeit präsentiert zwei Finite-Elemente-Methoden aus der Literat…
View article: Review of: Sindre Bangstad, Anders Breivik and the Rise of Islamophobia
Review of: Sindre Bangstad, Anders Breivik and the Rise of Islamophobia Open