This paper investigates numerical properties of a flux-based finite element method for the discretization of a SEIQRD (susceptible-exposed-infected-quarantined-recovered-deceased) model for the spread of COVID-19. The model is largely based on the SEIRD (susceptible-exposed-infected-recovered-deceased) models developed in recent works, with additional extension by a quarantined compartment of the living population and the resulting first-order system of coupled PDEs is solved by a Least-Squares meso-scale method. We incorporate several data on political measures for the containment of the spread gathered during the course of the year 2020 and develop an indicator that influences the predictions calculated by the method. The numerical experiments conducted show a promising accuracy of predictions of the space-time behavior of the virus compared to the real disease spreading data.

The nonconforming triangular piecewise quadratic finite element space by Fortin and Soulie can be used for the displacement approximation and its combination with discontinuous piecewise linear pressure elements is known to constitute a stable combination for incompressible linear elasticity computations. In this contribution, we extend the stress reconstruction procedure and resulting guaranteed a posteriori error estimator developed by Ainsworth, Allendes, Barrenechea and Rankin [2] and by Kim [18] to linear elasticity. In order to get a guaranteed reliability bound with respect to the energy norm involving only known constants, two modifications are carried out: (i) the stress reconstruction in next-to-lowest order Raviart-Thomas spaces is modified in such way that its anti-symmetric part vanishes in average on each element; (ii) the auxiliary conforming approximation is constructed under the constraint that its divergence coincides with the one for the nonconforming approximation. An important aspect of our construction is that all results hold uniformly in the incompressible limit. Global efficiency is also shown and the effectiveness is illustrated by adaptive computations involving different Lamé parameters including the incompressible limit case.

In this paper we discuss spectral properties of operators associated with the least-squares finite element approximation of elliptic partial differential equations. The convergence of the discrete eigenvalues and eigenfunctions towards the corresponding continuous eigenmodes is studied and analyzed with the help of appropriate L 2 error estimates. A priori and a posteriori estimates are proved.

A posteriori error estimates for the mixed numerical approximation of the Laplace eigenvalue problem can be derived using a reconstruction in the standard H 0 1 ‐conforming space for the primal variable of the mixed problem. In the case of Raviart–Thomas finite elements of arbitrary polynomial degree the resulting error estimator constitutes a guaranteed upper bound for the error and is shown to be local efficient. This paper shows that the extension for the BDM‐element is not straightforward.

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