Variational eigenvalue approximation of non-coercive operators with application to mixed formulations in elasticity

We present an abstract framework for the eigenvalue approximation of a class of non-coercive operators. We provide sufficient conditions to guarantee the spectral correctness of the Galerkin scheme and to obtain optimal rates of convergence. The theory is applied to the convergence analysis of mixed finite element approximations of the elasticity and Stokes eigensystems.

A priori error estimates for finite element approximations to transient convection-diffusion-reaction equations in fluidized beds

In this work, a priori error estimates for finite element approximations to the governing equations of heat and mass transfer in fluidized beds are derived. These equations are time dependent strongly coupled system of five semilinear convection-diffusion-reaction equations. The a priori error estimates for all the five variables are obtained for the error measured in L ∞(L 2) and L 2 ( E ) ${L}^{2}\left(\mathcal{E}\right)$ , E $\mathcal{E}$ is the energy norm.

Finite element-based assessment of energy harvesting in composite beams with piezoelectric transducers

A finite element-based methodology is introduced for studying composite beams with piezoelectric transducers connected to energy harvesting circuits. Continuous and lumped-parameter models are developed based on finite element approximations and verified by means of experiments performed on a cantilever beam subjected to sinusoidal excitation at low, with respect to resonance, frequencies below 15 Hz. Three harvesting circuits have been studied: an in-house, a commercial, modified to include a rectification stage, and an off-the-shelf commercial. Comparison of numerical predictions with experiments illustrates good agreement in voltage and high sensitivity to current losses in the circuit. It was found that the commercial circuits outperform the in-house circuit in terms of harvested power at frequencies higher than 5 Hz, while the latter enables power harvesting at arbitrary low frequencies. Based on these results, it is demonstrated that the developed approach enables coupled simulation of a composite structure and a realistic harvesting circuit in one-shot.

Accurate Full-Vectorial Finite Element Method Combined with Exact Non-Reflecting Boundary Condition for Computing Guided Waves in Optical Fibers

The vector electromagnetic problem for eigenwaves of optical fibers, originally formulated on the whole plane, is equivalently reduced to a linear parametric eigenvalue problem posed in a circle, convenient for numerical solution. The study of the solvability of this problem is based on the spectral theory of compact self-adjoint operators. Asymptotic properties of the dispersion curves and their smoothness are investigated for the new formulation of the problem. A numerical method based on finite element approximations combined with an exact non-reflecting boundary condition is developed. Error estimates for approximating eigenvalues and eigenfunctions are derived.