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h p -anisotropic mesh adaptation technique based on interpolation error estimates

Dolejší, Vít (2013)

Applications of Mathematics 2013

We present a completely new h p -anisotropic mesh adaptation technique for the numerical solution of partial differential equations with the aid of a discontinuous piecewise polynomial approximation. This approach generates general anisotropic triangular grids and the corresponding degrees of polynomial approximation based on the minimization of the interpolation error. We develop the theoretical background of this approach and present a numerical example demonstrating the efficiency of this anisotropic...

High resolution schemes for open channel flow

Brandner, Marek, Egermaier, Jiří, Kopincová, Hana (2010)

Programs and Algorithms of Numerical Mathematics

One of the commonly used models for river flow modelling is based on the Saint-Venant equations - the system of hyperbolic equations with spatially varying flux function and a source term. We introduce finite volume methods that solve this type of balance laws efficiently and satisfy some important properties at the same time. The properties like consistency, stability and convergence are necessary for the mathematically correct solution. However, the schemes should be also positive semidefinite...

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