Numerical Methods for PDEs: State of the Art Techniques

Description

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. Front Matter ....Pages i-xv An Introduction to Recent Developments in Numerical Methods for Partial Differential Equations (Daniele Antonio Di Pietro, Alexandre Ern, Luca Formaggia)....Pages 1-4 An Introduction to the Theory of M-Decompositions (Bernardo Cockburn, Guosheng Fu, Ke Shi)....Pages 5-29 Mimetic Spectral Element Method for Anisotropic Diffusion (Marc Gerritsma, Artur Palha, Varun Jain, Yi Zhang)....Pages 31-74 An Introduction to Hybrid High-Order Methods (Daniele Antonio Di Pietro, Roberta Tittarelli)....Pages 75-128 Distributed Lagrange Multiplier for Fluid-Structure Interactions (Daniele Boffi, Frédéric Hecht, Olivier Pironneau)....Pages 129-145 Generalization of the Pythagorean Eigenvalue Error Theorem and Its Application to Isogeometric Analysis (Michael Bartoň, Victor Calo, Quanling Deng, Vladimir Puzyrev)....Pages 147-170 Weakly Consistent Regularisation Methods for Ill-Posed Problems (Erik Burman, Lauri Oksanen)....Pages 171-202 Reduced Basis Approximation and A Posteriori Error Estimation: Applications to Elasticity Problems in Several Parametric Settings (Dinh Bao Phuong Huynh, Federico Pichi, Gianluigi Rozza)....Pages 203-247 Adaptive Tree Approximation with Finite Element Functions: A First Look (Andreas Veeser)....Pages 249-284 Defective Boundary Conditions for PDEs with Applications in Haemodynamics (Luca Formaggia, Christian Vergara)....Pages 285-312