Given a two dimensional oriented surface equipped with a simplicial mesh, the standard lowest order finite element spaces provide a complex Xâ€¢ centered on Raviart-Thomas divergence conforming vectorâ€¦ (More)

The development of smoothed projections, constructed by combining the canonical interpolation operators defined from the degrees of freedom with a smoothing operator, has proved to be an effectiveâ€¦ (More)

We elaborate on the interpretation of some mixed finite element spaces in terms of differential forms. First we develop a framework in which we show how tools from algebraic topology can be appliedâ€¦ (More)

The present paper serves to introduce a new robust modelling technique and solution methodology for a class of problems in structural optimization, in which we calculate the structural design thatâ€¦ (More)

The Galerkin discretization of the Electric Field Integral Equation is reinvestigated. We prove quasi-optimal convergence estimates at nonresonant frequencies, using orthogonal splittings of theâ€¦ (More)

We extend the preconditioning technique developed by O. Steinbach and W.L. Wendland in [8] to the Helmholtz equation which governs time harmonic acoustic waves. Using layer potentials to representâ€¦ (More)

We study the linearization of three dimensional Regge calculus around Euclidean metric. We provide an explicit formula for the corresponding quadratic form and relate it to the curlt curl operatorâ€¦ (More)