This volume gathers contributions from participants of the Introductory School and the IHP thematic quarter on Numerical Methods for PDE, held in 2016 in Cargese (Corsica) and Paris, providing an opportunity to disseminate the latest results and envisage fresh challenges in traditional and new application fields. Numerical analysis applied to the approximate solution of PDEs is a key discipline in applied mathematics, and over the last few years, several new paradigms have appeared, leading to entire new families of discretization methods and solution algorithms. This book is intended for researchers in the field.

1 Di Pietro D.A. et al, An introduction to the theory of M-decompositions.- 2 Gerritsma M. et al, Mimetic Spectral Element Method for Anisotropic Diffusion.- 3 Di Pietro D.A. and Tittarelli R., An introduction to Hybrid High-Order methods.- 4 Boffi D. et al, Distributed Lagrange multiplier for fluid-structure interactions.- 5 Barton M. et al, Generalization of the Pythagorean Eigenvalue Error Theorem and its Application to Isogeometric Analysis.- 6 Burman E. and Oksanen L., Weakly consistent regularisation methods for ill-posed problems.- 7 Phuong Huynh D.B. et al, Reduced basis approximation and a posteriori error estimation: applications to elasticity problems in several parametric settings.- 8 Veeser A., Adaptive Tree Approximation With Finite Element Functions – A First Look.- 9 Formaggia L. and Vergara C., Defective boundary conditions for PDEs with applications in haemodynamics.