A posteriori error estimates for the virtual element method

An a posteriori error analysis for the virtual element method (VEM) applied to general elliptic problems is presented. The resulting error estimator is of residual-type and applies on very general polygonal/polyhedral meshes. The estimator is fully computable as it relies only on quantities available from the VEM solution, namely its degrees of freedom and element-wise polynomial projection. Upper and lower bounds of the error estimator with respect to the VEM approximation error are proven. The error estimator is used to drive adaptive mesh refinement in a number of test problems. Mesh adaptation is particularly simple to implement since elements with consecutive co-planar edges/faces are allowed and, therefore, locally adapted meshes do not require any local mesh post-processing

Validation of Sample Preparation Methods for Microplastic Analysis in Wastewater Matrices—Reproducibility and Standardization

There is a growing interest in monitoring microplastics in the environment, corresponding to increased public concerns regarding their potential adverse effects on ecosystems. Monitoring microplastics in the environment is difficult due to the complex matrices that can prevent reliable analysis if samples are not properly prepared first. Unfortunately, sample preparation methods are not yet standardized, and the various efforts to validate them overlook key aspects. The goal of this study was to develop a sample preparation method for wastewater samples, which removes natural organic matter without altering the properties of microplastics. Three protocols, based on KOH, H2O2, and Fenton reactions, were chosen out of ten protocols after a literature review and pre-experiments. In order to investigate the effects of these reagents on seven polymers (PS, PE, PET, PP, PA, PVC, and PLA), this study employed µFTIR, laser diffraction-based particle size analysis, as well as TD-Pyr-GC/MS. Furthermore, the study discussed issues and inconsistencies with the Fenton reactions reported in the literature in previous validation efforts. The findings of this study suggest that both H2O2 and Fenton reactions are most effective in terms of organic matter removal from microplastic samples while not affecting the tested polymers, whereas KOH dissolved most PLA and PET particles