16 citations · 16 across the 11 of their papers we have counts for
14 papers
A ϕ-FEM approach for time-dependent domains with unfitted meshes
Michel Duprez, Johan Marguet, Alexei Lozinski +1
In this work, we propose an unfitted finite element scheme to approximate the solution of the heat equation on moving domains. We use the ϕ-FEM paradigm in which the computational…
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…
Embedded Trefftz DG method for the Helmholtz equation
Paul Stocker, Igor Voulis
We study an embedded Trefftz discontinuous Galerkin method for the Helmholtz equation. The method starts from a polynomial DG space and enforces the Trefftz property through local…
Adaptive stochastic Galerkin finite element methods: Optimality and non-affine coefficients
Markus Bachmayr, Henrik Eisenmann, Igor Voulis
Near-optimal computational complexity of an adaptive stochastic Galerkin method with independently refined spatial meshes for elliptic partial differential equations is shown. The…
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…
A convergent adaptive finite element stochastic Galerkin method based on multilevel expansions of random fields
Markus Bachmayr, Martin Eigel, Henrik Eisenmann +1
The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product p…
Analysis of divergence-preserving unfitted finite element methods for the mixed Poisson problem
Christoph Lehrenfeld, Tim van Beeck, Igor Voulis
In this paper we present a new H(div)-conforming unfitted finite element method for the mixed Poisson problem which is robust in the cut configuration and preserves conservation pr…
Time-Continuous and Time-Discontinuous Space-Time Finite Elements for Advection-Diffusion Problems
Max von Danwitz, Igor Voulis, Norbert Hosters +1
We construct four variants of space-time finite element discretizations based on linear tensor-product and simplex-type finite elements. The resulting discretizations are continuou…
An adaptive stochastic Galerkin method based on multilevel expansions of random fields: Convergence and optimality
Markus Bachmayr, Igor Voulis
The subject of this work is a new stochastic Galerkin method for second-order elliptic partial differential equations with random diffusion coefficients. It combines operator compr…
A time dependent Stokes interface problem: well-posedness and space-time finite element discretization
Igor Voulis, Arnold Reusken
In this paper a time dependent Stokes problem that is motivated by a standard sharp interface model for the fluid dynamics of two-phase flows is studied. This Stokes interface prob…
Discontinuous Galerkin Time Discretization Methods for Parabolic Problems with Linear Constraints
Igor Voulis, Arnold Reusken
We consider time discretization methods for abstract parabolic problems with inhomogeneous linear constraints. Prototype examples that fit into the general framework are the heat e…