## 32 Citations

On fractional Orlicz–Sobolev spaces

- Mathematics
- 2021

Some recent results on the theory of fractional Orlicz–Sobolev spaces are surveyed. They concern Sobolev type embeddings for these spaces with an optimal Orlicz target, related Hardy type…

Discontinuous Petrov–Galerkin boundary elements

- MathematicsNumerische Mathematik
- 2017

A discontinuous Petrov–Galerkin method with optimal test functions is established and its quasi-optimal convergence in related Sobolev norms is proved, which implies quasi-optimistic convergence in the $$L^2$$L2-norm.

On eigenmode approximation for Dirac equations: Differential forms and fractional Sobolev spaces

- MathematicsMath. Comput.
- 2018

Eigenmode convergence is proved, as well as optimal convergence orders, assuming a flat background metric on a periodic domain, in finite element spaces of differential forms.

Stable decompositions of hp-BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D

- Mathematics
- 2018

We consider fractional Sobolev spaces $H^\theta(\Gamma)$, $\theta \in [0,1]$ on a 2D surface $\Gamma$. We show that functions in $H^\theta(\Gamma)$ can be decomposed into contributions with local…

Local high-order regularization and applications to hp-methods

- MathematicsComput. Math. Appl.
- 2015

Raviart-Thomas Spaces

- Mathematics
- 2014

In this chapter we introduce Raviart–Thomas spaces, which constitute the most classical finite element subspaces of \(H(\mathrm{div};\varOmega )\), and prove their main interpolation and…

Discontinuous Galerkin $$hp$$-BEM with quasi-uniform meshes

- MathematicsNumerische Mathematik
- 2013

A discontinuous variant of the boundary element Galerkin method with quasi-uniform meshes is presented and a quasi-optimal error estimate is proved and convergence orders are concluded which are quasi-Optimal for the h-version with arbitrary degree and almost quasi- optimal for p-version.

Optimal adaptivity for a standard finite element method for the Stokes problem

- Computer Science, Mathematics
- 2017

It is proved that the a standard adaptive algorithm for the Taylor-Hood discretization of the stationary Stokes problem converges with optimal rate and a new connection is made between the mentioned quasi-orthogonality and $LU$-factorizations of infinite matrices.

Finite element quasi-interpolation and best approximation

- Mathematics
- 2015

This paper introduces a quasi-interpolation operator for scalar- and vector-valued finite element spaces constructed on affine, shape-regular meshes with some continuity across mesh interfaces.This…

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- Mathematics
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- Mathematics
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- Mathematics
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Localization of the Aronszajn-Slobodeckij norm and application to adaptive boundary element methods
Part II. The three-dimensional case

- MathematicsNumerische Mathematik
- 2002

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- Mathematics
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- Mathematics
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An adaptive boundary element method for the exterior Stokes problem in three dimensions

- Mathematics, Computer Science
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An adaptive refinement strategy for the h-version of the boundary element method with weakly singular operators on surfaces with optimal lower a priori error estimates for edge singularities on uniform and graded meshes is presented.