41 citations · 369 across the 28 of their papers we have counts for
28 papers · 1 filter
Optimal complexity of adaptive FEM for second-order linear elliptic PDEs driven by non-residual estimators, Part I: Symmetric PDEs
Philipp Bringmann, Aleksandar Dadic, Dario Ferloni +3
We consider adaptive finite element methods for symmetric second-order linear elliptic PDEs, where the adaptive algorithm steers the local mesh refinement as well as an iterative a…
Quasi-optimal complexity of iterative Galerkin methods driven by an elliptic reconstruction error estimator
Maximilian Brunner, Gregor Gantner, Christoph Lietz +1
We study an iterative Galerkin method for quasilinear elliptic problems in the Browder-Minty setting. The resulting discrete nonlinear systems are solved by linearization via a (da…
On -robust convergence and optimality of adaptive FEM driven by equilibrated-flux estimators
Théophile Chaumont-Frelet, Zhaonan Dong, Gregor Gantner +1
Building on existing -adaptive algorithms driven by equilibrated-flux estimators from [ESAIM Math. Model. Numer. Anal. 57 (2023), 329--366] and the references therein, we propo…
Optimal convergence rates of an adaptive finite element method for unbounded domains
Théophile Chaumont-Frelet, Gregor Gantner
We consider linear reaction-diffusion equations posed on unbounded domains, and discretized by adaptive Lagrange finite elements. To obtain finite-dimensional spaces, it is necessa…
Adaptive boundary element methods for regularized combined field integral equations
Théophile Chaumont-Frelet, Gregor Gantner
While the exterior Helmholtz problem with Dirichlet boundary conditions is always well-posed, the associated standard boundary integral equations are not if the squared wavenumber…
Inexpensive polynomial-degree-robust equilibrated flux a posteriori estimates for isogeometric analysis
Gregor Gantner, Martin Vohralík
We consider isogeometric discretizations of the Poisson model problem, focusing on high polynomial degrees and strong hierarchical refinements. We derive a posteriori error estimat…
Improved rates for a space-time FOSLS of parabolic PDEs
Gregor Gantner, Rob Stevenson
We consider the first-order system space-time formulation of the heat equation introduced in [Bochev, Gunzburger, Springer, New York (2009)], and analyzed in [Führer, Karkulik, Com…
Applications of a space-time FOSLS formulation for parabolic PDEs
Gregor Gantner, Rob Stevenson
In this work, we show that the space-time first-order system least-squares (FOSLS) formulation [Führer, Karkulik, Comput. Math. Appl. 92 (2021)] for the heat equation and its recen…
Stable implementation of adaptive IGABEM in 2D in MATLAB
Gregor Gantner, Dirk Praetorius, Stefan Schimanko
We report on our MATLAB program package IGABEM2D, which provides an easily accessible implementation of adaptive Galerkin boundary element methods in the frame of isogeometric anal…
A well-posed First Order System Least Squares formulation of the instationary Stokes equations
Gregor Gantner, Rob Stevenson
In this paper, a well-posed simultaneous space-time First Order System Least Squares formulation is constructed of the instationary incompressible Stokes equations with slip bounda…
Adaptive space-time BEM for the heat equation
Gregor Gantner, Raymond van Venetië
We consider the space-time boundary element method (BEM) for the heat equation with prescribed initial and Dirichlet data. We propose a residual-type a posteriori error estimator t…
Adaptive BEM for elliptic PDE systems, part II: Isogeometric analysis with hierarchical B-splines for weakly-singular integral equations
Gregor Gantner, Dirk Praetorius
We formulate and analyze an adaptive algorithm for isogeometric analysis with hierarchical B-splines for weakly-singular boundary integral equations. We prove that the employed wei…
Mathematical foundations of adaptive isogeometric analysis
Annalisa Buffa, Gregor Gantner, Carlotta Giannelli +2
This paper reviews the state of the art and discusses recent developments in the field of adaptive isogeometric analysis, with special focus on the mathematical theory. This includ…
Efficient numerical approximation of a non-regular Fokker--Planck equation associated with first-passage time distributions
Udo Boehm, Sonja Cox, Gregor Gantner +1
In neuroscience, the distribution of a decision time is modelled by means of a one-dimensional Fokker--Planck equation with time-dependent boundaries and space-time-dependent drift…
Goal-oriented adaptive finite element methods with optimal computational complexity
Roland Becker, Gregor Gantner, Michael Innerberger +1
We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-r…
Plain convergence of adaptive algorithms without exploiting reliability and efficiency
Gregor Gantner, Dirk Praetorius
We consider h-adaptive algorithms in the context of the finite element method (FEM) and the boundary element method (BEM). Under quite general assumptions on the building blocks SO…
Further results on a space-time FOSLS formulation of parabolic PDEs
Gregor Gantner, Rob Stevenson
In [2019, Space-time least-squares finite elements for parabolic equations, arXiv:1911.01942] by Führer& Karkulik, well-posedness of a space-time First-Order System Least-Squares f…
Adaptive BEM for elliptic PDE systems, Part I: Abstract framework for weakly-singular integral equations
Gregor Gantner, Dirk Praetorius
In the present work, we consider weakly-singular integral equations arising from linear second-order strongly-elliptic PDE systems with constant coefficients, including, e.g., line…
Rate optimality of adaptive finite element methods with respect to the overall computational costs
Gregor Gantner, Alexander Haberl, Dirk Praetorius +1
We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formula…
Adaptive IGAFEM with optimal convergence rates: T-splines
Gregor Gantner, Dirk Praetorius
We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations…
Adaptive isogeometric boundary element methods with local smoothness control
Gregor Gantner, Dirk Praetorius, Stefan Schimanko
In the frame of isogeometric analysis, we consider a Galerkin boundary element discretization of the hyper-singular integral equation associated with the 2D Laplacian. We propose a…
Optimal additive Schwarz preconditioning for adaptive 2D IGA boundary element methods
Thomas Führer, Gregor Gantner, Dirk Praetorius +1
We define and analyze (local) multilevel diagonal preconditioners for isogeometric boundary elements on locally refined meshes in two dimensions. Hypersingular and weakly-singular…
Optimal convergence behavior of adaptive FEM driven by simple (h-h/2)-type error estimators
Christoph Erath, Gregor Gantner, Dirk Praetorius
For some Poisson-type model problem, we prove that adaptive FEM driven by the (h-h/2)-type error estimators from [Ferraz-Leite, Ortner, Praetorius, Numer. Math. 116 (2010)] leads t…
Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines
Gregor Gantner, Daniel Haberlik, Dirk Praetorius
We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations…