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Adaptive modeling for free-surface flows

Simona Perotto (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

This work represents a first step towards the simulation of the motion of water in a complex hydrodynamic configuration, such as a channel network or a river delta, by means of a suitable “combination” of different mathematical models. In this framework a wide spectrum of space and time scales is involved due to the presence of physical phenomena of different nature. Ideally, moving from a hierarchy of hydrodynamic models, one should solve throughout the whole domain the most complex model (with...

Adaptive multiresolution methods

Margarete O. Domingues, Sônia M. Gomes, Olivier Roussel, Kai Schneider (2011)

ESAIM: Proceedings

These lecture notes present adaptive multiresolution schemes for evolutionary PDEs in Cartesian geometries. The discretization schemes are based either on finite volume or finite difference schemes. The concept of multiresolution analyses, including Harten’s approach for point and cell averages, is described in some detail. Then the sparse point representation method is discussed. Different strategies for adaptive time-stepping, like local scale dependent time stepping and time step control, are...

Adaptive Multiresolution Methods: Practical issues on Data Structures, Implementation and Parallelization*

K. Brix, S. Melian, S. Müller, M. Bachmann (2011)

ESAIM: Proceedings

The concept of fully adaptive multiresolution finite volume schemes has been developed and investigated during the past decade. Here grid adaptation is realized by performing a multiscale decomposition of the discrete data at hand. By means of hard thresholding the resulting multiscale data are compressed. From the remaining data a locally refined grid is constructed. The aim of the present work is to give a self-contained overview on the construction of an appropriate multiresolution analysis using...

Aerodynamic Computations Using a Finite Volume Method with an HLLC Numerical Flux Function

L. Remaki, O. Hassan, K. Morgan (2011)

Mathematical Modelling of Natural Phenomena

A finite volume method for the simulation of compressible aerodynamic flows is described. Stabilisation and shock capturing is achieved by the use of an HLLC consistent numerical flux function, with acoustic wave improvement. The method is implemented on an unstructured hybrid mesh in three dimensions. A solution of higher order accuracy is obtained by reconstruction, using an iteratively corrected least squares process, and by a new limiting procedure....

An a posteriori error analysis for dynamic viscoelastic problems

J. R. Fernández, D. Santamarina (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, a dynamic viscoelastic problem is numerically studied. The variational problem is written in terms of the velocity field and it leads to a parabolic linear variational equation. A fully discrete scheme is introduced by using the finite element method to approximate the spatial variable and an Euler scheme to discretize time derivatives. An a priori error estimates result is recalled, from which the linear convergence is derived under suitable regularity conditions. Then, an a posteriori...

An a posteriori error analysis for dynamic viscoelastic problems

J. R. Fernández, D. Santamarina (2011)

ESAIM: Mathematical Modelling and Numerical Analysis


In this paper, a dynamic viscoelastic problem is numerically studied. The variational problem is written in terms of the velocity field and it leads to a parabolic linear variational equation. A fully discrete scheme is introduced by using the finite element method to approximate the spatial variable and an Euler scheme to discretize time derivatives. An a priori error estimates result is recalled, from which the linear convergence is derived under suitable regularity conditions. Then, an a posteriori error...

An adaptive finite element method for solving a double well problem describing crystalline microstructure

Andreas Prohl (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The minimization of nonconvex functionals naturally arises in materials sciences where deformation gradients in certain alloys exhibit microstructures. For example, minimizing sequences of the nonconvex Ericksen-James energy can be associated with deformations in martensitic materials that are observed in experiments[2,3]. — From the numerical point of view, classical conforming and nonconforming finite element discretizations have been observed to give minimizers with their quality being highly dependent...

An adaptive finite element method in reconstruction of coefficients in Maxwell's equations from limited observations

Larisa Beilina, Samar Hosseinzadegan (2016)

Applications of Mathematics

We propose an adaptive finite element method for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions in the Maxwell's system using limited boundary observations of the electric field in 3D. We derive a posteriori error estimates in the Tikhonov functional to be minimized and in the regularized solution of this functional, as well as formulate the corresponding adaptive algorithm. Our numerical experiments...

An Adaptive Multi-level method for Convection Diffusion Problems

Martine Marion, Adeline Mollard (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this article we introduce an adaptive multi-level method in space and time for convection diffusion problems. The scheme is based on a multi-level spatial splitting and the use of different time-steps. The temporal discretization relies on the characteristics method. We derive an a posteriori error estimate and design a corresponding adaptive algorithm. The efficiency of the multi-level method is illustrated by numerical experiments, in particular for a convection-dominated problem.

An analysis of the influence of data extrema on some first and second order central approximations of hyperbolic conservation laws

Michael Breuss (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We discuss the occurrence of oscillations when using central schemes of the Lax-Friedrichs type (LFt), Rusanov’s method and the staggered and non-staggered second order Nessyahu-Tadmor (NT) schemes. Although these schemes are monotone or TVD, respectively, oscillations may be introduced at local data extrema. The dependence of oscillatory properties on the numerical viscosity coefficient is investigated rigorously for the LFt schemes, illuminating also the properties of Rusanov’s method. It turns...

An analysis of the influence of data extrema on some first and second order central approximations of hyperbolic conservation laws

Michael Breuss (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We discuss the occurrence of oscillations when using central schemes of the Lax-Friedrichs type (LFt), Rusanov's method and the staggered and non-staggered second order Nessyahu-Tadmor (NT) schemes. Although these schemes are monotone or TVD, respectively, oscillations may be introduced at local data extrema. The dependence of oscillatory properties on the numerical viscosity coefficient is investigated rigorously for the LFt schemes, illuminating also the properties of Rusanov's method. It turns...

An approximate nonlinear projection scheme for a combustion model

Christophe Berthon, Didier Reignier (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The paper deals with the numerical resolution of the convection-diffusion system which arises when modeling combustion for turbulent flow. The considered model is of compressible turbulent reacting type where the turbulence-chemistry interactions are governed by additional balance equations. The system of PDE’s, that governs such a model, turns out to be in non-conservation form and usual numerical approaches grossly fail in the capture of viscous shock layers. Put in other words, classical finite...

An approximate nonlinear projection scheme for a combustion model

Christophe Berthon, Didier Reignier (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The paper deals with the numerical resolution of the convection-diffusion system which arises when modeling combustion for turbulent flow. The considered model is of compressible turbulent reacting type where the turbulence-chemistry interactions are governed by additional balance equations. The system of PDE's, that governs such a model, turns out to be in non-conservation form and usual numerical approaches grossly fail in the capture of viscous shock layers. Put in other words, classical finite...

Currently displaying 181 – 200 of 310