97 citations · 381 across the 25 of their papers we have counts for
33 papers
Space-time finite element interpolation of nonsmooth functions satisfying boundary conditions
Thomas Führer, Gregor Gantner, Roberto González +1
We construct Scott-Zhang-type space-time quasi-interpolation operators on tensor- product meshes for parabolic settings. Specifically, these are linear and uniformly bounded projec…
A space-time finite element method for parabolic obstacle problems
José Joaquín Carvajal, Davood Damircheli, Thomas Führer +2
We propose and analyze a general framework for space-time finite element methods that is based on least-squares finite element methods for solving a first-order reformulation of th…
Space-time FEM-BEM couplings for parabolic transmission problems
Thomas Führer, Gregor Gantner, Michael Karkulik
We develop couplings of a recent space-time first-order system least-squares (FOSLS) method for parabolic problems and space-time boundary element methods (BEM) for the heat equati…
Efficient estimation for a smoothing thin plate spline in a two-dimensional space
Joaquin Cavieres, Michael Karkulik
Using a deterministic framework allows us to estimate a function with the purpose of interpolating data in spatial statistics. Radial basis functions are commonly used for scattere…
Well-posedness of first-order acoustic wave equations and space-time finite element approximation
Thomas Führer, Roberto González, Michael Karkulik
We study a first-order system formulation of the (acoustic) wave equation and prove that the operator of this system is an isomorphsim from an appropriately defined graph space to…
On interpolation spaces of piecewise polynomials on mixed meshes
Michael Karkulik, Jens Markus Melenk, Alexander Rieder
We consider fractional Sobolev spaces , , on 2D domains and -conforming discretizations by globally continuous piecewise polynomials on a mesh consisting of s…
Least-squares finite elements for distributed optimal control problems
Thomas Führer, Michael Karkulik
We provide a framework for the numerical approximation of distributed optimal control problems, based on least-squares finite element methods. Our proposed method simultaneously so…
Space-time finite element methods for parabolic distributed optimal control problems
Thomas Führer, Michael Karkulik
We present a method for the numerical approximation of distributed optimal control problems constrained by parabolic partial differential equations. We complement the first-order o…
MINRES for second-order PDEs with singular data
Thomas Führer, Norbert Heuer, Michael Karkulik
Minimum residual methods such as the least-squares finite element method (FEM) or the discontinuous Petrov--Galerkin method with optimal test functions (DPG) usually exclude singul…
Analysis of backward Euler primal DPG methods
Thomas Führer, Norbert Heuer, Michael Karkulik
We analyse backward Euler time stepping schemes for the primal DPG formulation of a class of parabolic problems. Optimal error estimates are shown in the natural norm and in the $L…
Local convergence of the FEM for the integral fractional Laplacian
Markus Faustmann, Michael Karkulik, Jens Markus Melenk
We provide for first order discretizations of the integral fractional Laplacian sharp local error estimates on proper subdomains in both the local -norm and the localized ener…
Space-time least-squares finite elements for parabolic equations
Thomas Führer, Michael Karkulik
We present a space-time least squares finite element method for the heat equation. It is based on residual minimization in L2 norms in space-time of an equivalent first order syste…
A finite element method for elliptic Dirichlet boundary control problems
Michael Karkulik
We consider the finite element discretization of an optimal Dirichlet boundary control problem for the Laplacian, where the control is considered in . To avoid computin…
Stable decompositions of -BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D
Michael Karkulik, Jens Markus Melenk, Alexander Rieder
We consider fractional Sobolev spaces , , on a 2D surface . We show that functions in can be decomposed into contributions with local support in a s…
-matrix approximability of inverses of discretizations of the fractional Laplacian
Michael Karkulik, Jens Markus Melenk
The integral version of the fractional Laplacian on a bounded domain is discretized by a Galerkin approximation based on piecewise linear functions on a quasi-uniform mesh. We show…
New a priori analysis of first-order system least-squares finite element methods for parabolic problems
Thomas Führer, Michael Karkulik
We provide new insights into the a priori theory for a time-stepping scheme based on least-squares finite element methods for parabolic first-order systems. The elliptic part of th…
Combining the DPG method with finite elements
Thomas Führer, Norbert Heuer, Michael Karkulik +1
We propose and analyze a discretization scheme that combines the discontinuous Petrov-Galerkin and finite element methods. The underlying model problem is of general diffusion-adve…
Variational formulation of time-fractional parabolic equations
Michael Karkulik
We consider initial/boundary value problems for time-fractional parabolic PDE of order with Caputo fractional derivative (also called fractional diffusion equations in the…
A robust DPG method for singularly perturbed reaction-diffusion problems
Norbert Heuer, Michael Karkulik
We present and analyze a discontinuous Petrov-Galerkin method with optimal test functions for a reaction-dominated diffusion problem in two and three space dimensions. We start wit…
On the coupling of DPG and BEM
Thomas Führer, Norbert Heuer, Michael Karkulik
We develop and analyze strategies to couple the discontinuous Petrov-Galerkin method with optimal test functions to (i) least-squares boundary elements and (ii) various variants of…
DPG method with optimal test functions for a fractional advection diffusion equation
Vincent J. Ervin, Thomas Führer, Norbert Heuer +1
We develop an ultra-weak variational formulation of a fractional advection diffusion problem in one space dimension and prove its well-posedness. Based on this formulation, we defi…
Local inverse estimates for non-local boundary integral operators
Markus Aurada, Michael Feischl, Thomas Führer +3
We prove local inverse-type estimates for the four non-local boundary integral operators associated with the Laplace operator on a bounded d-dimensional Lipschitz domain Omega for…
DPG method with optimal test functions for a transmission problem
Norbert Heuer, Michael Karkulik
We propose and analyze a numerical method to solve an elliptic transmission problem in full space. The method consists of a variational formulation involving standard boundary inte…
Local high-order regularization and applications to hp-methods
Michael Karkulik, Jens Markus Melenk
We develop a regularization operator based on smoothing on a locally defined length scale. This operator is defined on and has approximation properties that are given by the…