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Full Description
The last few years have witnessed a surge in the development and usage of discretization methods supporting general meshes in geoscience applications. The need for general polyhedral meshes in this context can arise in several situations, including the modelling of petroleum reservoirs and basins, CO2 and nuclear storage sites, etc. In the above and other situations, classical discretization methods are either not viable or require ad hoc modifications that add to the implementation complexity. Discretization methods able to operate on polyhedral meshes and possibly delivering arbitrary-order approximations constitute in this context a veritable technological jump. The goal of this monograph is to establish a state-of-the-art reference on polyhedral methods for geoscience applications by gathering contributions from top-level research groups working on this topic. This book is addressed to graduate students and researchers wishing to deepen their knowledge ofadvanced numerical methods with a focus on geoscience applications, as well as practitioners of the field.
Contents
J. Droniou et al., Non-conforming finite elements on polytopal meshes.- C. Cancès et al., Error estimates for the gradient discretization method on degenerate parabolic equations of porous medium type.- K. Brenner et al., Nodal discretization of two-phase discrete fracture matrix models.- Jan M. Nordbotten and E. Keilegavlen, An introduction to multi-point flux (MPFA) and stress (MPSA) finite volume methods for thermo-poroelasticity.- Paola F. Antonietti et al., High-order discontinuous Galerkin methods on polyhedral grids for geophysical applications: seismic wave propagation and fractured reservoir simulations.- L. Botti et al., A hybrid high-order method for multiple-network poroelasticity.- D. Adak et al., The mixed virtual element method for the Richards equation.- A. Fumagalli et al., Performances of the mixed virtual element method on complex grids for underground flow.
