12 citations · 26 across the 8 of their papers we have counts for
8 papers
Adaptive hybrid high-order method for guaranteed lower eigenvalue bounds
Carsten Carstensen, Benedikt Gräßle, Ngoc Tien Tran
The higher-order guaranteed lower eigenvalue bounds of the Laplacian in the recent work by Carstensen, Ern, and Puttkammer [Numer. Math. 149, 2021] require a parameter $C_{\mathrm{…
Rate-optimal higher-order adaptive conforming FEM for biharmonic eigenvalue problems on polygonal domains
Carsten Carstensen, Benedikt Gräßle
The a posteriori error analysis of the classical Argyris finite element methods dates back to 1996, while the optimal convergence rates of associated adaptive finite element scheme…
Pressure-improved Scott-Vogelius type elements
Nis-Erik Bohne, Benedikt Gräßle, Stefan A. Sauter
The Scott-Vogelius element is a popular finite element for the discretization of the Stokes equations which enjoys inf-sup stability and gives divergence-free velocity approximatio…
Unifying a posteriori error analysis of five piecewise quadratic discretisations for the biharmonic equation
Carsten Carstensen, Benedikt Gräßle, Neela Nataraj
An abstract property (H) is the key to a complete a priori error analysis in the (discrete) energy norm for several nonstandard finite element methods in the recent work [Lowest-or…
A posteriori error control for fourth-order semilinear problems with quadratic nonlinearity
Carsten Carstensen, Benedikt Gräßle, Neela Nataraj
A general a posteriori error analysis applies to five lowest-order finite element methods for two fourth-order semi-linear problems with trilinear non-linearity and a general sourc…
The pressure-wired Stokes element: a mesh-robust version of the Scott-Vogelius element
Benedikt Gräßle, Nis-Erik Bohne, Stefan A. Sauter
The Scott-Vogelius finite element pair for the numerical discretization of the stationary Stokes equation in 2D is a popular element which is based on a continuous velocity approxi…
Stabilization-free HHO a posteriori error control
Fleurianne Bertrand, Carsten Carstensen, Benedikt Gräßle +1
The known a posteriori error analysis of hybrid high-order methods (HHO) treats the stabilization contribution as part of the error and as part of the error estimator for an effici…
Optimal multilevel adaptive FEM for the Argyris element
Benedikt Gräßle
The main drawback for the application of the conforming Argyris FEM is the labourious implementation on the one hand and the low convergence rates on the other. If no appropriate a…