Publications

• Article dans une revue

Stereolithography

Marion Dehurtevent, Lieven Robberecht, Jean-Christophe Hornez, Anthony Thuault, Etienne Deveaux, Pascal Béhin

Objectives : The aim of this study was to compare the physical and mechanical properties of stereolithography (SLA)- manufactured alumina ceramics of different composition to those of subtractive- manufactured ceramics and to produce suitable dental crown frameworks. Methods : The physical and…

Dental Materials, 2017, 33 (5), pp.477-485. ⟨10.1016/j.dental.2017.01.018⟩. ⟨hal-03079726⟩

• Article dans une revue

An <em>hp</em>-FEM for Singularly Perturbed Transmission Problems

Serge Nicaise, Xenophontos Christos

We perform the analysis of the hp finite element approximation for the solution to singularly perturbed transmission problems, using Spectral Boundary Layer Meshes. In [12] it was shown that this method yields robust exponential convergence, as the degree p of the approximating polynomials is…

• Article dans une revue

Four-dimensional locally strongly convex homogeneous affine hypersurfaces

Abdelouahab Chikh Salah, Luc Vrancken

We study four-dimensional locally strongly convex, locally homogeneous, hypersurfaces whose affine shape operator has two distinct principal curvatures. In case that one of the eigenvalues has dimension 1 these hypersurfaces have been previously studied in Dillen and Vrancken (Math Z 212:61–72,…

Journal of Geometry, 2017, 108 (1), pp.119-147. ⟨10.1007/s00022-016-0330-6⟩. ⟨hal-03146492⟩

• Article dans une revue

Optimization and pre-clinical perception of an artificial simulator for endodontic training : a preliminary study

Lieven Robberecht, Jean-Christophe Hornez, Marion Dehurtevent, Thomas Dufour, Julien Labreuche, Etienne Deveaux, Feng Chai

The aim of this study was to evaluate the performance of ceramic, hybrid ceramic, and commercial plastic bloc root canal simulator (RCS) as preclinical training aids in the learning phase of endodontic treatments. A previously developed hydroxyapatite ceramic RCS was improved by adding epoxy resin…

Journal of Dental Education, 2017, 81 (3), pp.326-332. ⟨10.1002/j.0022-0337.2017.81.3.tb06278.x⟩. ⟨hal-03120963⟩

• Article dans une revue

δ ] (2, 2)-ideal centroaffine hypersurfaces of dimension 5

Handan Yildirim, Luc Vrancken

The notion of an ideal submanifold was introduced by Chen at the end of the last century. A survey of recent results in this area can be found in his book [9]. Recently, in [10], an optimal collection of Chen's inequalities was obtained for Lagrangian submanifolds in complex space forms. As…

Taiwanese Journal of Mathematics, TJM, 2017, 21 (2), pp.283-304. ⟨10.11650/tjm/7809⟩. ⟨hal-03184684⟩

• Article dans une revue

On four-dimensional Einstein affine hyperspheres

Zejun Hu, Haizhong Li, Luc Vrancken

It is well-known that Vrancken–Li–Simon classified locally strongly convex affine hyperspheres in Rn+1 whose affine metric are of constant sectional curvatures, but on the other side it is still a difficult problem to classify n-dimensional locally strongly convex affine hyperspheres whose affine…

Differential Geometry and its Applications, 2017, 50, pp.20-33. ⟨10.1016/j.difgeo.2016.10.003⟩. ⟨hal-03172966⟩

• Article dans une revue

Regularity and a priori error analysis of a Ventcel problem in polyhedral domains

Serge Nicaise, Hengguang Li, Anna L. Mazzucato

We consider the regularity of a mixed boundary value problem for the Laplace operator on a polyhedral domain, where Ventcel boundary conditions are imposed on one face of the polyhedron and Dirichlet boundary conditions are imposed on the complement of that face in the boundary. We establish…

Mathematical Methods in the Applied Sciences, 2017, 40 (5), ⟨10.1002/mma.4083⟩. ⟨hal-01332720v3⟩

• Article dans une revue

Surfaces in a pseudo-sphere with harmonic or 1-type pseudo-spherical Gauss map.

B. Bektas, J. van Der Veken, Luc Vrancken

We give a complete classification of Riemannian and Lorentzian surfaces of arbitrary codimension in a pseudo-sphere whose pseudo-spherical Gauss maps are of 1-type or, in particular, harmonic. In some cases a concrete global classification is obtained, while in other cases the solutions are…

Ann. Global Anal. Geom., 2017, 52, pp.45-55. ⟨10.1007/s10455-017-9548-2⟩. ⟨hal-03233877⟩

• Article dans une revue

Convergence and stability analyses of hierarchic models of dissipative second order evolution equations

Serge Nicaise

We perform some hierarchical analyses of dissipative systems. For that purpose, we first propose a general abstract setting, prove a convergence result and discuss some stability properties. This abstract setting is then illustrated by significant examples of damped (acoustic) wave equations for…

Collectanea Mathematica, 2017, 68 (3), pp.433-462. ⟨10.1007/s13348-017-0192-8⟩. ⟨hal-03152027⟩

• Article dans une revue

Adapted Numerical Methods for the Poisson Equation with $L^2$ Boundary Data in NonConvex Domains

Thomas Apel, Serge Nicaise, Johannes Pfefferer

The very weak solution of the Poisson equation with L 2 boundary data is defined by the method of transposition. The finite element solution with regularized boundary data converges in the L 2 (Ω)-norm with order 1/2 in convex domains but has a reduced convergence order in nonconvex domains…

SIAM Journal on Numerical Analysis, 2017, 55 (4), pp.1937-1957. ⟨10.1137/16m1062077⟩. ⟨hal-01957588⟩