output
19962022
most citedThe VOLNA code for the numerical modelling of tsunami waves: generation, propagation and inundation

107 citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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11 papers · 1 filter

math.NA2020

A Class of Collocated Finite Volume Schemes for Incompressible Flow Problems

R. Eymard, R. Herbin, J. -C Latché +1

In this paper, we present a class of finite volume schemes for incompressible flow problems. The unknowns are collocated at the center of the control volumes, and the stability of…

math.NA2019★ 7 cited

On the multi-symplectic structure of Boussinesq-type systems. II: Geometric discretization

Angel Durán, Denys Dutykh, Dimitrios Mitsotakis

In this paper we consider the numerical approximation of systems of Boussinesq-type to model surface wave propagation. Some theoretical properties of these systems (multi-symplecti…

math.NA2019

The gradient discretisation method for linear advection problems

Jérôme Droniou, Robert Eymard, T. Gallouët +1

We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equation…

math.NA2016★ 11 cited

How to overcome the Courant-Friedrichs-Lewy condition of explicit discretizations?

Denys Dutykh

This manuscript contains some thoughts on the discretization of the classical heat equation. Namely, we discuss the advantages and disadvantages of explicit and implicit schemes. T…

math.NA2016★ 2 cited

A brief introduction to pseudo-spectral methods: application to diffusion problems

Denys Dutykh

The topic of these notes could be easily expanded into a full one-semester course. Nevertheless, we shall try to give some flavour along with theoretical bases of spectral and pseu…

math.NA2015★ 14 cited

Numerical simulation of conservation laws with moving grid nodes: Application to tsunami wave modelling

Gayaz Khakimzyanov, Denys Dutykh, Dimitrios Mitsotakis +1

In the present article we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension combined with appropriate predictor-corrector meth…

math.NA2015★ 18 cited

On supraconvergence phenomenon for second order centered finite differences on non-uniform grids

Gayaz Khakimzyanov, Denys Dutykh

In the present study we consider an example of a boundary value problem for a simple second order ordinary differential equation, which may exhibit a boundary layer phenomenon. We…

math.NA2014

Kinetic entropy inequality and hydrostatic reconstruction scheme for the Saint-Venant system

Emmanuel Audusse, François Bouchut, Marie-Odile Bristeau +1

A lot of well-balanced schemes have been proposed for discretizing the classical Saint-Venant system for shallow water flows with non-flat bottom. Among them, the hydrostatic recon…

math.NA2009★ 2 cited

Singular limit of a two-phase flow problem in porous medium as the air viscosity tends to zero

Robert Eymard, Marie Henry, Danielle Hilhorst

In this paper we consider a two-phase flow problem in porous media and study its singular limit as the viscosity of the air tends to zero; more precisely, we prove the convergence…

math.NA2007★ 1 cited

Weak order for the discretization of the stochastic heat equation

Arnaud Debussche, Jacques Printems

In this paper we study the approximation of the distribution of Hilbert--valued stochastic process solution of a linear parabolic stochastic partial differential equation wri…

math.NA2006

A mixed finite volume scheme for anisotropic diffusion problems on any grid

Jérôme Droniou, Robert Eymard

We present a new finite volume scheme for anisotropic heterogeneous diffusion problems on unstructured irregular grids, which simultaneously gives an approximation of the solution…