Publications related to Interior penalty continuous and discontinuous finite element approximations of hyperbolic equations

Mimetic scalar products of discrete differential forms

We propose a strategy for the systematic construction of the mimetic inner products on cochain spaces for the numerical approximation of partial differential equations on unstructured polygonal and polyhedral meshes. The mimetic inner products are locally ...

2014

Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems

Assyr Abdulle, Gilles Vilmart

A fully discrete analysis of the finite element heterogeneous multiscale method for a class of nonlinear elliptic homogenization problems of nonmonotone type is proposed. In contrast to previous results obtained for such problems in dimension

d\leq2

for ...

Amer Mathematical Soc2014

Stable multi-domain spectral penalty methods for fractional partial differential equations

Jan Sickmann Hesthaven

We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any ord ...

Elsevier2014

Mathematical analysis of variational isogeometric methods

Annalisa Buffa, Rafael Vazquez Hernandez

This review paper collects several results that form part of the theoretical foundation of isogeometric methods. We analyse variational techniques for the numerical resolution of PDEs based on splines or NURBS and we provide optimal approximation and error ...

2014

Modelling of the hygroelastic behaviour of normal and compression wood tracheids

Razvan Cristian Neagu

Compression wood conifer tracheids show different swelling and stiffness properties than those of usual normal wood, which has a practical function in the living plant: when a conifer shoot is moved from its vertical position, compression wood is formed in ...

Elsevier2014

Measurement of the Position-Dependent Electrophoretic Force on DNA in a Glass Nanocapillary

Aleksandra Radenovic, Lorenz Jan Steinbock, Roman Bulushev, Sergey Khlybov

The electrophoretic force on a single DNA molecule inside a glass nanocapillary depends on the opening size and varies with the distance along the symmetrical axis of the nanocapillary. Using optical tweezers and DNA-coated beads, we measured the stalling ...

American Chemical Society2014

Optimal control for Partial Differential Equations

Antoine Giovanni Imboden

In this project report, we first present the application of the finite elements method to the numerical approximation of elliptic and parabolic PDEs over two-dimensional domains. We then consider the theory and numerical approximation of optimal control pr ...

2013

Numerical Approximation Of Internal Discontinuity Interface Problems

Alfio Quarteroni, Marco Discacciati, Samuel Quinodoz

This work focuses on the finite element discretization of boundary value problems whose solution features either a discontinuity or a discontinuous conormal derivative across an interface inside the computational domain. The interface is characterized via ...

Siam Publications2013

Mechanisms of Fano Resonances in Coupled Plasmonic Systems

Olivier Martin, Andrea Lovera, Benjamin Gallinet

Fano resonances in hybridized systems formed from the interaction of bright modes only are reported. Despite precedent works, we demonstrate theoretically and experimentally that Fano resonances can be obtained by destructive interference between two brigh ...

Amer Chemical Soc2013

Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity

Alfio Quarteroni, Ricardo Esteban Ruiz Baier, Davide Baroli

In this paper we present a discontinuous Galerkin method applied to incompressible nonlinear elastostatics in a total Lagrangian deformation-pressure formulation, for which a suitable interior penalty stabilization is applied. We prove that the proposed di ...

Springer Verlag2013

Interior penalty continuous and discontinuous finite element approximations of hyperbolic equations

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Mimetic scalar products of discrete differential forms

Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems

Stable multi-domain spectral penalty methods for fractional partial differential equations

Mathematical analysis of variational isogeometric methods

Modelling of the hygroelastic behaviour of normal and compression wood tracheids

Measurement of the Position-Dependent Electrophoretic Force on DNA in a Glass Nanocapillary

Optimal control for Partial Differential Equations

Numerical Approximation Of Internal Discontinuity Interface Problems

Mechanisms of Fano Resonances in Coupled Plasmonic Systems

Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity

Mathematical analysis of variational isogeometric methods

Mimetic scalar products of discrete differential forms

Optimal control for Partial Differential Equations

Numerical Approximation Of Internal Discontinuity Interface Problems

Mechanisms of Fano Resonances in Coupled Plasmonic Systems

Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity

Stable multi-domain spectral penalty methods for fractional partial differential equations

Modelling of the hygroelastic behaviour of normal and compression wood tracheids

Measurement of the Position-Dependent Electrophoretic Force on DNA in a Glass Nanocapillary

Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems