246 citations · 467 across the 24 of their papers we have counts for
29 papers
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…
Unified a priori analysis of four second-order FEM for fourth-order quadratic semilinear problems
Carsten Carstensen, Neela Nataraj, Gopikrishnan C. Remesan +1
A unified framework for fourth-order semilinear problems with trilinear nonlinearity and general source allows for quasi-best approximation with lowest-order finite element methods…
Local parameter selection in the interior penalty method for the biharmonic equation
Philipp Bringmann, Carsten Carstensen, Julian Streitberger
The symmetric interior penalty method is one of the most popular discontinuous Galerkin methods for the biharmonic equation. This paper introduces an automatic local selectio…
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…
Nonconforming virtual elements for the biharmonic equation with Morley degrees of freedom on polygonal meshes
Carsten Carstensen, Rekha Khot, Amiya K. Pani
The lowest-order nonconforming virtual element extends the Morley triangular element to polygons for the approximation of the weak solution to the biharmonic equ…
Stability of mixed FEMs for non-selfadjoint indefinite second-order linear elliptic PDEs
C. Carstensen, Neela Nataraj, Amiya K. Pani
For a well-posed non-selfadjoint indefinite second-order linear elliptic PDE with general coefficients in and symmetric and uniformly positive d…
Adaptive guaranteed lower eigenvalue bounds with optimal convergence rates
Carsten Carstensen, Sophie Puttkammer
Guaranteed lower Dirichlet eigenvalue bounds (GLB) can be computed for the -th Laplace operator with a recently introduced extra-stabilized nonconforming Crouzeix-Raviart (…
Convergent adaptive hybrid higher-order schemes for convex minimization
Carsten Carstensen, Ngoc Tien Tran
This paper proposes two convergent adaptive mesh-refining algorithms for the hybrid high-order method in convex minimization problems with two-sided p-growth. Examples include the…
Critical Functions and Inf-Sup Stability of Crouzeix-Raviart Elements
C. Carstensen, S. Sauter
In this paper, we prove that Crouzeix-Raviart finite elements of polynomial order , odd, are inf-sup stable for the Stokes problem on triangulations. For , …
Direct guaranteed lower eigenvalue bounds with optimal a priori convergence rates for the bi-Laplacian
Carsten Carstensen, Sophie Puttkammer
An extra-stabilised Morley finite element method (FEM) directly computes guaranteed lower eigenvalue bounds with optimal a priori convergence rates for the bi-Laplace Dirichlet eig…
A priori and a posteriori error analysis of the Crouzeix-Raviart and Morley FEM with original and modified righthand sides
Carsten Carstensen, Neela Nataraj
This article on nonconforming schemes for harmonic problems simultaneously treats the Crouzeix-Raviart () and the Morley finite elements () for the original and for m…
Lowest-order equivalent nonstandard finite element methods for biharmonic plates
Carsten Carstensen, Neela Nataraj
The popular (piecewise) quadratic schemes for the biharmonic equation based on triangles are the nonconforming Morley finite element, the discontinuous Galerkin, the interior…
A priori and a posteriori error analysis of the lowest-order NCVEM for second-order linear indefinite elliptic problems
Carsten Carstensen, Rekha Khot, Amiya K. Pani
The nonconforming virtual element method (NCVEM) for the approximation of the weak solution to a general linear second-order non-selfadjoint indefinite elliptic PDE in a polygonal…
Morley Finite Element Method for the von Kármán Obstacle Problem
Carsten Carstensen, Sharat Gaddam, Neela Nataraj +2
This paper focusses on the von Kármán equations for the moderately large deformation of a very thin plate with the convex obstacle constraint leading to a coupled system of semilin…
Adaptive Morley FEM for the von Kármán equations with optimal convergence rates
Carsten Carstensen, Neela Nataraj
The adaptive nonconforming Morley finite element method (FEM) approximates a regular solution to the von Kármán equations with optimal convergence rates for sufficiently fine trian…
How to prove the discrete reliability for nonconforming finite element methods
Carsten Carstensen, Sophie Puttkammer
Optimal convergence rates of adaptive finite element methods are well understood in terms of the axioms of adaptivity. One key ingredient is the discrete reliability of a residual-…
Nonlinear discontinuous Petrov-Galerkin methods
Carsten Carstensen, Philipp Bringmann, Friederike Hellwig +1
The discontinuous Petrov-Galerkin method is a minimal residual method with broken test spaces and is introduced for a nonlinear model problem in this paper. Its lowest-order versio…
Constants in Discrete Poincaré and Friedrichs Inequalities and Discrete Quasi-Interpolation
Carsten Carstensen, Friederike Hellwig
This paper provides a discrete Poincaré inequality in space dimensions on a simplex with explicit constants. This inequality bounds the norm of the piecewise derivative of…
A Priori and A Posteriori Error Control of Discontinuous Galerkin Finite Element Methods for the Von Kármán Equations
Carsten Carstensen, Gouranga Mallik, Neela Nataraj
This paper analyses discontinuous Galerkin finite element methods (DGFEM) to approximate a regular solution to the von Kármán equations defined on a polygonal domain. A discrete in…
Interaction of martensitic microstructures in adjacent grains
John M. Ball, Carsten Carstensen
It is often observed that martensitic microstructures in adjacent polycrystal grains are related. For example, micrographs of Arlt exhibit propagation of layered structures across…
Nonconforming Finite Element Discretisation for Semilinear Problems with Trilinear Nonlinearity
Carsten Carstensen, Gouranga Mallik, Neela Nataraj
The Morley finite element method (FEM) is attractive for semilinear problems with the biharmonic operator as a leading term in the stream function vorticity formulation of 2D Navie…
Residual-based a posteriori error analysis for symmetric mixed Arnold-Winther FEM
C. Carstensen, D. Gallistl, J. Gedicke
This paper introduces an explicit residual-based a posteriori error analysis for the symmetric mixed finite element method in linear elasticity after Arnold-Winther with pointwise…
Axioms of adaptivity for separate marking
Carsten Carstensen, Hella Rabus
Mixed finite element methods with flux errors in -norms and div-least-squares finite element methods require a separate marking strategy in obligatory adaptive mesh-refinin…
Breaking spaces and forms for the DPG method and applications including Maxwell equations
C. Carstensen, L. Demkowicz, J. Gopalakrishnan
Discontinuous Petrov Galerkin (DPG) methods are made easily implementable using `broken' test spaces, i.e., spaces of functions with no continuity constraints across mesh element i…