  Partial differential equations can be solved on general polygonal and
polyhedral meshes, through Polytopal Element Methods (PEMs). Unfortunately, the
relation between geometry and analysis is still unknown and subject to ongoing
research in order to identify weaker shape-regularity criteria under which PEMs
can reliably work. We propose PEMesh, a graphical framework to support the
analysis of the relation between the geometric properties of polygonal meshes
and the numerical performances of PEM solvers. PEMesh allows the design of
polygonal meshes that increasingly stress some geometric properties, by
exploiting any external PEM solver, and supports the study of the correlation
between the performances of such a solver and geometric properties of the input
mesh. Furthermore, it is highly modular, customisable, easy to use, and
provides the possibility to export analysis results both as numerical values
and graphical plots. PEMesh has a potential practical impact on ongoing and
future research activities related to PEM methods, polygonal mesh generation
and processing.
