Virtual Element in environmental flow problems: operator preserving, coupling of phenomena and adaptivity
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Polygonal and Polyhedral methods can facilitate the meshing process in problems with very complex domains bypassing one of the major difficulties in this kind of simulation. However, the presence of stabilization terms common in these methods sometimes violates the physical nature of the phenomenon, moreover, very complex domains can still induce elements of bad quality. For this reason, adaptive methods, that can improve the quality of the final mesh, can be useful, as well as stabilization-free VEM formulations and the use of orthogonal polynomial bases. In the present talk, we will tackle several of these issues and discuss their use to some environmental applications, i.e. in the field of geothermal energy and plant growth in partially saturated porous media. Suitable effective implementation of these methods is a fundamental aspect that will be considered.
