34 citations · 113 across the 10 of their papers we have counts for
11 papers
Pressure-robust error estimate of optimal order for the Stokes equations on domains with edges
Thomas Apel, Volker Kempf
The velocity solution of the incompressible Stokes equations is not affected by changes of the right hand side data in form of gradient fields. Most mixed methods do not replicate…
A nonconforming pressure-robust finite element method for the Stokes equations on anisotropic meshes
Thomas Apel, Volker Kempf, Alexander Linke +1
Most classical finite element schemes for the (Navier-)Stokes equations are neither pressure-robust, nor are they inf-sup stable on general anisotropic triangulations. A lack of pr…
Brezzi-Douglas-Marini interpolation of any order on anisotropic triangles and tetrahedra
Thomas Apel, Volker Kempf
Recently, the -conforming finite element families for second order elliptic problems have come more into focus, since due to hybridization and subseque…
Regularity of the solution of the scalar Signorini problem in polygonal domains
Thomas Apel, Serge Nicaise
The Signorini problem for the Laplace operator is considered in a general polygonal domain. It is proved that the coincidence set consists of a finite number of boundary parts plus…
Error estimates for Dirichlet control problems in polygonal domains
Thomas Apel, Mariano Mateos, Johannes Pfefferer +1
The paper deals with finite element approximations of elliptic Dirichlet boundary control problems posed on two-dimensional polygonal domains. Error estimates are derived for the a…
Adapted numerical methods for the numerical solution of the Poisson equation with boundary data in non-convex domains
Thomas Apel, Serge Nicaise, Johannes Pfefferer
The very weak solution of the Poisson equation with boundary data is defined by the method of transposition. The finite element solution with regularized boundary data conver…