Preface

Discretization methods of Partial Differential Equations (PDEs) that support polygonal or polyhedral (in short, polytopal) grids have been receiving extensive interest in recent years. Polytopal grids offer, for instance, a natural framework to handle hanging nodes, different cell shapes within the same mesh, and non-matching interfaces resulting from local mesh adaptation or from multi-domain mesh gluing. Polytopal grids often lead to enhanced computational efficiency owing to the flexibility provided in the geometrical approximation of the domain and of the problem. Interesting natural applications include basin and reservoir simulation, problems with moving boundaries (as encountered in fluid-structure interaction, crack propagation and contact problems), materials with complex inclusions, topology optimization, image processing, and many others.