The Discontinuous Galerkin Time Domain (DGTD) methods are now popular for the solution of wave propagation problems. Able to deal with unstructured, possibly locally-refined meshes, they handleeasily complex geometries and remain fully explicit with easy parallelization and extension to high orders of accuracy. Non-dissipative versions exist, where some discrete electromagnetic energy is exactly conserved. However, the stability limit of the methods, related to the smallest elements in the mesh, calls for the construction of local-time stepping algorithms. These schemes have already been developed for N-body mechanical problems and are known as symplectic schemes. They are applied here to DGTD methods on wave propagation problems.

In this paper we develop a residual based a posteriori error analysis for an augmentedmixed finite element method applied to the problem of linear elasticity in the plane.More precisely, we derive a reliable and efficient a posteriori error estimator for thecase of pure Dirichlet boundary conditions. In addition, several numericalexperiments confirming the theoretical properties of the estimator, andillustrating the capability of the corresponding adaptive algorithm to localize the singularities and the large stress regions of the solution, are also reported.

This paper proposes and analyzes a BEM-FEM scheme to approximatea time-harmonic diffusion problem in the plane with non-constantcoefficients in a bounded area. The model is set as a Helmholtztransmission problem with adsorption and with non-constantcoefficients in a bounded domain. We reformulate the problem as afour-field system. For the temperature and the heat flux we usepiecewise constant functions and lowest order Raviart-Thomaselements associated to a triangulation approximating the boundeddomain. For the boundary unknowns we take spaces of periodicsplines. We show how to transmit information from the approximateboundary to the exact one in an efficient way and provewell-posedness of the Galerkin method. Error estimates areprovided and experimentally corroborated at the end of the work.

We consider the Stokes problem provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We write a variational formulation of this problem with three independent unknowns: the vorticity, the velocity and the pressure. Next we propose a discretization by spectral element methods which relies on this formulation. A detailed numerical analysis leads to optimal error estimates for the three unknowns and numerical experiments confirm the interest of the discretization.


In recent years several papers have been devoted to stabilityand smoothing properties in maximum-norm offinite element discretizations of parabolic problems.Using the theory of analytic semigroups it has been possibleto rephrase such properties as bounds for the resolventof the associated discrete elliptic operator. In all thesecases the triangulations of the spatial domain has beenassumed to be quasiuniform. In the present paper weshow a resolvent estimate, in one and two space dimensions,under weaker conditions on the triangulations than quasiuniformity.In the two-dimensional case, the bound for the resolvent containsa logarithmic factor.


We consider models based on conservation laws. For the optimizationof such systems, a sensitivity analysis is essential to determinehow changes in the decision variables influence the objectivefunction. Here we study the sensitivity with respect to the initialdata of objective functions that depend upon the solution of Riemannproblems with piecewise linear flux functions. We presentrepresentations for the one–sided directional derivatives of theobjective functions. The results can be used in the numerical methodcalled Front-Tracking.