We introduce a high-order spline geometric approach for the initial boundary value problem for Maxwell's equations. The method is geometric in the sense that it discretizes in structure preserving fashion the two de Rham sequences of differential forms inv ...
The propagation of fluid driven fractures is used in a number of industrial applications (well stimulation of unconventional reservoirs, development of deep geothermal systems) but also occurs naturally (magmatic dyke intrusion). While the mechanics of hyd ...
In the framework of Performance Based Earthquake Engineering (PBEE), assessing the inelastic behaviour of structures both at the global (force-displacement) and local (stress-strain) level is of priority importance. This goal is typically achieved by advan ...
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 ...
We consider finite-energy equivariant solutions for the wave map problem from ℝ2+1 to S2 which are close to the soliton family. We prove asymptotic orbital stability for a codimension-two class of initial data which is small with respect to a stronger topo ...
We introduce a new family of explicit integrators for stiff Ito stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer from th ...
The research work reported in this dissertation is aimed to develop efficient and stable numerical schemes in order to obtain accurate numerical solution for viscoelastic fluid flows within the spectral element context. The present research consists in the ...
We consider a discontinuous Galerkin finite element method for the advection– reaction equation in two space–dimensions. For polynomial approximation spaces of degree greater than or equal to two on triangles we propose a method where stability is obtained ...
