The Hybrid High-Order Method for Polytopal Meshes

Daniele A. Di Pietro has been a Full Professor since 2012 and Deputy Director of Institut Montpellierain Alexander Grothendieck at the University of Montpellier (France) since 2019. He is the author of two research monographs published by Springer and more than 80 scientific papers in refereed international journals or conference proceedings. His research fields include the development and analysis of advanced numerical methods for partial differential equations, with applications to fluid and solid mechanics and porous media. Over the course of his career, he has supervised ten PhD students and six postdoctoral fellows. Jerome Droniou was a Full Professor in France before moving to Monash university (Australia), where he has been an Associate Professor in the School of Mathematics since 2018, and head of the applied and computational section since 2019. He has authored two research monographs and more than 80 peer-reviewed articles and conference proceedings on theoretical and numerical analysis of partial differential equations. His current research interests revolve around the development of numerical methods for complex applications, and the design of mathematical tools to analyse the convergence of these methods. He has supervised a dozen PhD students and postdoctoral fellows in France and Australia.

Part I: Foundations.- 1 Setting.- 2 Basic principles of Hybrid High-Order methods: The Poisson problem.- 3 Variable di_usion and di_usion-advection-reaction.- 4 Complements on pure di_usion.- 5 Variations and comparison with other methods.- Part II: Applications to advanced models.- 6 p-Laplacian and Leray-Lions.- 7 Linear elasticity.- 8 Stokes.- 9 Navier-Stokes.- Part III: Appendix.- 10 Appendix A: Error analysis setting for schemes in fully discrete formulation.- 11 Appendix B: Implementation.