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.
Daniele Antonio Di Pietro is Full Professor of Numerical Analysis at the Institut Montpelliérain Alexander Grothendieck at the University of Montpellier. He received his Ph.D. in Computational Fluid Mechanics from the University of Bergamo. 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. He is author of one book and over 50 research papers in peer-reviewed journals.
Alexandre Ern is a Senior Researcher at Ecole Nationale des Ponts et Chaussees (France) and at INRIA, and he holds a part-time Professor position in Numerical Analysis at Ecole Polytechnique (France). His contributions encompass mathematical modeling and numerical analysis in computational fluid and solid mechanics with applications in problems related to the environment and energy production. From 2006 to 2012, he has chaired the French National Research Program on Underground nuclear waste storage, and he has ongoing collaborations with several industrial partners. Alexandre Ern has authored three books and over 130 papers in peer-reviewed journals, and he has supervised about 20 PhD students working now in academia or industry.
Luca Formaggia is Professor of Numerical Analysis at the Modelling and Scientific Computing Laboratory (MOX) of the Department of Mathematics of Politecnico di Milano. His scientific work addresses the study of numerical methods for partial differential equations, scientific computing, computational fluid dynamics with applications to computational geosciences, biomedicine and industrial problems. He is the author of more than 90 articles and editor of several books. Currently he is the President of the Italian Society of Applied and Industrial Mathematics and was the Head of the MOX Laboratory from 2012 to 2016.
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.