7 papers
-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…
-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…
An energy-decreasing algorithm for the finite element approximation of ferronematic equilibrium states
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…
-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…
Damped energy-norm a posteriori error estimates for fully discrete approximations of the wave equation using C2-reconstructions with the leapfrog scheme
T. Chaumont-Frelet, A. Ern
We derive a posteriori error estimates for the the scalar wave equation discretized in space by continuous finite elements and in time by the explicit leapfrog scheme. Our analysis…