Narrow Results

A residual-based a posteriori error estimate for the Poisson problem with discontinuous diffusivity coefficient is derived in the case of a virtual element discretization. The error is measured considering a suitable polynomial projection of the discrete solution to prove an equivalence between the defined error and a computable residual based error estimator that does not involve any term related to the virtual element stabilization. Numerical results display a very good behavior of the ratio between the error and the error estimator, resulting independent of the meshsize and element distortion.

This paper presents a genetic algorithm based procedure for automatic identification of crack profiles. In the procedure geometric modeling technique is applied to incorporate crack(s) into the structure under evaluation and a geometric model is generated. The geometric model is then used to generate finite element mesh. In solving forward problems, finite element meshes are adapted based on error estimation to improve accuracy in computed structural responses. Numerical results show that error from solving forward problems can largely slow down GA convergence and significantly affect the accuracy of estimated crack parameters. Mesh adaptation can effectively reduce the error, thus speeding up the convergence and improving accuracy.

The mass transfer enhancement (MTE) by a single emulsion droplet subjected to a Poiseuille flow is studied by using h-adaptive finite element approximation. The Navier–Stokes equations with the surface tension force at a droplet–fluid phase for the fluid flows are considered. The mass transfer is modeled by convection–diffusion equation. The interface capturing method with a conservative level set approach is employed to track the interface of a droplet. This is also incorporated with a mesh adaptivity for increasing the resolution in vicinity of the interface of the droplet. We numerically investigate the effect of hydrodynamic interactions of the droplet with the fluid on the mass transfer in varying physical parameters of the fluid flows and the suspended droplet in order to find the optimum conditions to invoke the enhanced MTE. It is found that Pe is an important factor to enhance the mass transfer transported by the convective current with diffusion. It is also found that Ca is an important factor for MTE considering disturbances and deformability of the droplet during the mass transfer process. It is found that the MTE decreases with increasing Ca in a high concentration region ($C=0.9$) while MTE does not depend much on Ca in a low concentration region ($C=0.1$).