Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects

This first volume of the proceedings of the 8th conference on "Finite Volumes for Complex Applications" (Lille, June 2017) covers various topics including convergence and stability analysis, as well as investigations of these methods from the point of view of compatibility with physical principles. It collects together the focused invited papers comparing advanced numerical methods for Stokes and Navier-Stokes equations on a benchmark, as well as reviewed contributions from internationally leading researchers in the field of analysis of finite volume and related methods, offering a comprehensive overview of the state of the art in the field. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation, and recent decades have brought significant advances in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications. The book is a valuable resource for researchers, PhD and master's level students in numerical analysis, scientific computing and related fields such as partial differential equations, as well as engineers working in numerical modeling and simulations.

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PART 1. Invited Papers. Chi-Wang Shu, Bound-preserving high order finite volume schemes for conservation laws and convection-diffusion equations.-E.D. Fernandez-Nieto, Some geophysical applications with finite volume solvers of two-layer and two-phase systems.-Thierry Gallouet, Some discrete functional analysis tools.-Yuanzhen Cheng, Alina Chertock and Alexander Kurganov, A Simple Finite-Volume Method on a Cartesian Mesh for Pedestrian Flows with Obstacles.- PART 2. Franck Boyer and Pascal Omnes, Benchmark on discretization methods for viscous incompressible flows. Benchmark proposal for the FVCA8 conference : Finite Volume methods for the Stokes and Navier-Stokes equations.-Louis Vittoz, Guillaume Oger, Zhe Li, Matthieu De Leffe and David Le Touze, A high-order Finite Volume solver on locally refined Cartesian meshes.-Daniele A. Di Pietro and Stella Krell, Benchmark session : The 2D Hybrid High-Order method.-Jerome Droniou and Robert Eymard, Benchmark: two HybridMimetic Mixed schemes for the lid-driven cavity.-Eric Chenier, Robert Eymard and Raphaele Herbin, Results with a locally refined MAC scheme - benchmark session.-Sarah Delcourte and Pascal Omnes, Numerical results for a discrete duality finite volume discretization applied to the Navier-Stokes equations.-Franck Boyer and Stella Krell and Flore Nabet, Benchmark session : The 2D Discrete Duality Finite Volume Method.-P.-E. Angeli, M.-A. Puscas, G. Fauchet and A. Cartalade, FVCA8 benchmark for the Stokes and Navier-Stokes equations with the TrioCFD code - benchmark session.-PART 3. Theoretical Aspects of Finite Volumes. Franc oise Foucher, Moustafa Ibrahim and Mazen Saad, Analysis of a Positive CVFE Scheme For Simulating Breast Cancer Development, Local Treatment and Recurrence.-Christoph Erath and Dirk Praetorius, Céa-type quasi-optimality and convergence rates for (adaptive) vertexcentered FVM.-Helene Mathis and Nicolas Therme, Numerical convergence for a diffusive limit of the Goldstein-Taylor system on bounded domain.-Florian De Vuyst, Lagrange-Flux schemes and the entropy property.-Caterina Calgaro and Meriem Ezzoug, $L^\infty$-stability of IMEX-BDF2 finite volume scheme for convection diffusion equation.-Raphaele Herbin, Jean-Claude Latche and Khaled Saleh, Low Mach number limit of a pressure correction MAC scheme for compressible barotropic flows.-T. Gallouet, R. Herbin, J.-C. Latche and K. Mallem, Convergence of the MAC scheme for variable density flows.-J. Droniou, J. Hennicker, R. Masson, Uniform-in-time convergence of numerical schemes for a two-phase discrete fracture model.-Claire Chainais-Hillairet, Benoit Merlet and Antoine Zurek, Design and analysis of a finite volume scheme for a concrete carbonation model.-Rita Riedlbeck, Daniele A. Di Pietro, and Alexandre Ern, Equilibrated stress reconstructions for linear elasticity problems with application to a posteriori error analysis.-Patricio Farrell and Alexander Linke, Uniform Second Order Convergenceof a Complete Flux Scheme on Nonuniform 1D Grids.-J. Droniou and R. Eymard, The asymmetric gradient discretisation method.-Robert Eymard and Cindy Guichard, DGM, an item of GDM.-Claire Chainais-Hillairet, Benoit Merlet and Alexis F. Vasseur, Positive lower bound for the numerical solution of a convection-diffusion equation.-Franc ois Dubois, Isabelle Greff and Charles Pierre, Raviart Thomas Petrov Galerkin Finite Elements.-Naveed Ahmed, Alexander Linke, and Christian Merdon, Towards pressure-robust mixed methods for the incompressible Navier-Stokes equations.-Thierry Goudon, Stella Krell and Giulia Lissoni, Numerical analysis of the DDFV method for the Stokes problem with mixed Neumann/Dirichlet boundary conditions.-J. Droniou, R. Eymard, T. Gallouet, C. Guichard and R. Herbin, An error estimate for the approximation of linear parabolic equations by the Gradient Discretization Method.-M. Bessemoulin-Chatard, C. Chainais-Hillairet, and A. Jungel, Uniform $L^\infty$ estimates for approximate solutions of the bipolar driftdiffusion system.-Abdallah Bradji, Some convergence results of a multi-dimensional finite volume scheme for a time-fractional diffusion-wave equation.-Nina Aguillon and Franck Boyer, Optimal order of convergence for the upwind scheme for the linear advection on a bounded domain.-Matus Tibensky, Angela Handlovicova, Numerical scheme for regularised Riemannian mean curvature flow equation.-Ahmed Ait Hammou Oulhaj, A finite volume scheme for a seawater intrusion model.-Clement Cances and Flore Nabet, Finite volume approximation of a degenerate immiscible two-phase flow model of Cahn-Hilliard type.-Clement Cances, Claire Chainais-Hillairet and Stella Krell, A nonlinear Discrete Duality Finite Volume Scheme for convection-diffusion equations.-Wasilij Barsukow, Stationarity and vorticity preservation for the linearized Euler equations in multiple spatial dimensions.-Jan Giesselmann and Tristan Pryer, Goal-oriented error analysis of a DG scheme for a secondgradient elastodynamics model.-Alain Prignet, Simplified model for the clarinet and numerical schemes.- Author Index.