Announcement. Tony Humphries is delighted to announce his engagement to Rosa Almeida, who he met whilst travelling in Portugal after the conference. Abstract. We compute general (non-radial) positive solutions of the semi-linear elliptic PDE u+u+ u 5 = 0, in 3 space dimensions (where the nonlinearity is critical) using the Finite Element Method. We have overcome two fundamental diiculties in th...

Super convergence of the gradient of approximate solutions to second order elhptic équations is analysed and justified for a large ciass of curved isoparametric quadrilatéral éléments Résumé — On analyse et on justifie la super convergence du gradient des solutions approchées obtenues lors de la résolution d'équations elliptiques du second ordre à Vaide d'éléments isoparamétriques courbes de ty...

In finite element lore the term “unstable discretization” is often applied to situations when approximate solutions develop unphysical “wiggles”, or otherwise behave in a strange manner. A textbook example of such wiggles are Galerkin solutions of a scalar hyperbolic equation with discontinuous data. A more subtle example of instability is the “strange” behavior of mixed finite elements for the...

of the ordinary differential equation which occurs in the boundary condition. An exact nonreflecting boundary condition was derived previously for use with the time dependent wave equation in three Finally, we shall solve a sequence of scattering problems space dimensions. Here it is shown how to combine that boundary by using an explicit finite difference method and our condition with finite d...

A posteriori error estimates for the nonconforming P1 element are easily determined by the hypercircle method via Marini’s observation on the relation to the mixed method of Raviart–Thomas. Another tool is Ainsworth’s application of the hypercircle method to mixed methods. The relation on the finite element solutions is also extended to an a priori relation of the errors, and the errors of four...

The Reissner-Mindlin model is frequently used by engineers for plates and shells of small to moderate thickness. This model is well known for its “locking” phenomenon so that many numerical approximations behave poorly when the thickness parameter tends to zero. Following the formulation derived by Brezzi and Fortin, we construct a new finite element scheme for the Reissner-Mindlin model using ...

In this paper, we study the convergence and time evolution of the error between the discontinuous Galerkin (DG) finite element solution and the exact solution for conservation laws when upwind fluxes are used. We prove that if we apply piecewise linear polynomials to a linear scalar equation, the DG solution will be superconvergent towards a particular projection of the exact solution. Thus, th...

Abstract. This article is devoted to the study of the finite element approximation for a nonlocal nonlinear parabolic problem. Using a linearised Crank-Nicolson Galerkin finite element method for a nonlinear reaction-diffusion equation, we establish the convergence and error bound for the fully discrete scheme. Moreover, important results on exponential decay and vanishing of the solutions in f...