Mathematical modelling of the effects of mitotic inhibitors on avascular tumour growth.
Matrix transformation method of approximate solution of partial differential equations
Maximum norm error estimates in the finite element method with isoparametric quadratic elements and numerical integration
Maximum-Norm Stability and Error Estimates in Galerkin Methods for Parabolic Equations in One Space Variable
Medical image – based computational model of pulsatile flow in saccular aneurisms
Saccular aneurisms, swelling of a blood vessel, are investigated in order (i) to estimate the development risk of the wall lesion, before and after intravascular treatment, assuming that the pressure is the major factor, and (ii) to better plan medical interventions. Numerical simulations, using the finite element method, are performed in three-dimensional aneurisms. Computational meshes are derived from medical imaging data to take into account both between-subject and within-subject anatomical...
Medical image – based computational model of pulsatile flow in saccular aneurisms
Saccular aneurisms, swelling of a blood vessel, are investigated in order (i) to estimate the development risk of the wall lesion, before and after intravascular treatment, assuming that the pressure is the major factor, and (ii) to better plan medical interventions. Numerical simulations, using the finite element method, are performed in three-dimensional aneurisms. Computational meshes are derived from medical imaging data to take into account both between-subject and within-subject anatomical...
Mesh independent superlinear convergence estimates of the conjugate gradient method for some equivalent self-adjoint operators
A mesh independent bound is given for the superlinear convergence of the CGM for preconditioned self-adjoint linear elliptic problems using suitable equivalent operators. The results rely on K-condition numbers and related estimates for compact Hilbert-Schmidt operators in Hilbert space.
Mesh r-adaptation for unilateral contact problems
We present a mesh adaptation method by node movement for two-dimensional linear elasticity problems with unilateral contact. The adaptation is based on a hierarchical estimator on finite element edges and the node displacement techniques use an analogy of the mesh topology with a spring network. We show, through numerical examples, the efficiency of the present adaptation method.
Mesh Refinement For Stabilized Convection Diffusion Equations
We derive a residual a posteriori error estimates for the subscales stabilization of convection diffusion equation. The estimator yields upper bound on the error which is global and lower bound that is local
Method of fundamental solutions for biharmonic equation based on Almansi-type decomposition
The aim of this paper is to analyze mathematically the method of fundamental solutions applied to the biharmonic problem. The key idea is to use Almansi-type decomposition of biharmonic functions, which enables us to represent the biharmonic function in terms of two harmonic functions. Based on this decomposition, we prove that an approximate solution exists uniquely and that the approximation error decays exponentially with respect to the number of the singular points. We finally present results...
Method of interior boundaries in a mixed problem of acoustic scattering.
Méthode de calcul du coefficient de singularité pour la solution du problème de Laplace dans un domaine diédral
Méthode d’éléments finis pour la résolution numérique de problèmes extérieurs en dimension
Méthodes d'éléments finis avec intégration numérique pour des problèmes elliptiques du quatrième ordre
Méthodes multipas pour des équations paraboliques non linéaires.
Méthodes numériques pour les équations de Navier-Stokes instationnaires des fluides visqueux incompressibles
Mimetic finite differences for elliptic problems
We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent norm are derived.
Mimetic finite differences for elliptic problems
We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent H1 norm are derived.
Minimization of functional majorant in a posteriori error analysis based on (div) multigrid-preconditioned CG method.
Minimizing Oseen-Frank energy for nematic liquid crystals : algorithms and numerical results