TY - BOOK TI - The Gradient Discretisation Method T3 - Mathématiques et Applications,, ISSN 1154-483X ; ; 82 AU - Droniou, Jérôme., szerző A2 - Eymard, Robert., szerző A2 - Gallouët, Thierry., szerző A2 - Guichard, Cindy., szerző A2 - Herbin, Raphaèle., szerző PB - Cham : : Springer International Publishing : : Imprint: Springer PY - 2018 LA - angol SN - 978-3-319-79042-8 SN - 1154-483X ; ET - 1st ed. 2018. N1 - This monograph presents the Gradient Discretisation Method (GDM), which is a unified convergence analysis framework for numerical methods for elliptic and parabolic partial differential equations. The results obtained by the GDM cover both stationary and transient models; error estimates are provided for linear (and some non-linear) equations, and convergence is established for a wide range of fully non-linear models (e.g. Leray–Lions equations and degenerate parabolic equations such as the Stefan or Richards models). The GDM applies to a diverse range of methods, both classical (conforming, non-conforming, mixed finite elements, discontinuous Galerkin) and modern (mimetic finite differences, hybrid and mixed finite volume, MPFA-O finite volume), some of which can be built on very general meshes.