7 papers · 1 filter
An energy-decreasing algorithm for the finite element approximation of ferronematic equilibrium states and its numerical realization
Alexandre Ern, Ruma R. Maity
We develop an energy-decreasing algorithm for the finite element approximation of two-dimensional ferronematic equilibrium states. The problem is formulated as the minimization of…
Bounded, Commuting, Discrete-trace Preserving Projections
Alexandre Ern, Johnny Guzmán, Pratyush Potu
We construct bounded, commuting projections for the three-dimensional de Rham complex with the additional property that the projections preserve the trace of functions/fields if th…
-a posteriori error estimates for hybrid high-order methods applied to biharmonic problems
Zhaonan Dong, Alexandre Ern, Tanvi Wadhawan
We derive a residual-based -a posteriori error estimator for hybrid high-order (HHO) methods on simplicial meshes applied to the biharmonic problem posed on two- and three-dime…
-reconstruction of piecewise polynomial fields with application to -a posteriori nonconforming error analysis for Maxwell's equations
Zhaonan Dong, Alexandre Ern
We devise and analyse a novel -reconstruction operator for piecewise polynomial fields on shape-regular simplicial meshes. The (non-polynomial) recon…
A priori and a posteriori analysis of the discontinuous Galerkin approximation of the time-harmonic Maxwell's equations under minimal regularity assumptions
T. Chaumont-Frelet, A. Ern
We derive a priori and a posteriori error estimates for the discontinuous Galerkin (dG) approximation of the time-harmonic Maxwell's equations. Specifically, we consider an interio…
-error analysis of mixed-order hybrid high-order methods for elliptic problems on simplicial meshes
Zhaonan Dong, Alexandre Ern
We present both -a priori and -a posteriori error analysis of a mixed-order hybrid high-order (HHO) method to approximate second-order elliptic problems on simplicial meshe…
Bridging the Multiscale Hybrid-Mixed and Multiscale Hybrid High-Order methods
T. Chaumont-Frelet, A. Ern, S. Lemaire +1
We establish the equivalence between the Multiscale Hybrid-Mixed (MHM) and the Multiscale Hybrid High-Order (MsHHO) methods for a variable diffusion problem with piecewise polynomi…