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Displaying similar documents to “Book review: 'Numerical Solutions of Partial Differential Equations' by S. Bertoluzza, S. Falletta, G. Ruso and Chi-Wang Shu”

On some composite schemes of time integration in structural dynamics

Vala, Jiří

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Numerical simulations of time-dependent behaviour of advances structures need the analysis of systems of partial differential equations of hyperbolic type, whose semi-discretization, using the Fourier multiplicative decomposition together with the finite element or similar techniques, leads to large sparse systems of ordinary differential equations. Effective and robust methods for numerical evaluation of their solutions in particular time steps are required; thus still new computational...

A new reconstruction-enhanced discontinuous Galerkin method for time-dependent problems

Kučera, Václav

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This work is concerned with the introduction of a new numerical scheme based on the discontinuous Galerkin (DG) method. We propose to follow the methodology of higher order finite volume schemes and introduce a reconstruction operator into the DG scheme. This operator constructs higher order piecewise polynomial reconstructions from the lower order DG scheme. Such a procedure was proposed already in [2] based on heuristic arguments, however we provide a rigorous derivation, which justifies...

Accurate numerical discretizations of non-conservative hyperbolic systems

Ulrik Skre Fjordholm, Siddhartha Mishra (2012)

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

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We present an alternative framework for designing efficient numerical schemes for non-conservative hyperbolic systems. This approach is based on the design of entropy conservative discretizations and suitable numerical diffusion operators that mimic the effect of underlying viscous mechanisms. This approach is illustrated by considering two model non-conservative systems: Lagrangian gas dynamics in non-conservative form and a form of isothermal Euler equations. Numerical experiments...

Accurate numerical discretizations of non-conservative hyperbolic systems

Ulrik Skre Fjordholm, Siddhartha Mishra (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

We present an alternative framework for designing efficient numerical schemes for non-conservative hyperbolic systems. This approach is based on the design of entropy conservative discretizations and suitable numerical diffusion operators that mimic the effect of underlying viscous mechanisms. This approach is illustrated by considering two model non-conservative systems: Lagrangian gas dynamics in non-conservative form and a form of isothermal Euler equations. Numerical experiments...