The first volume of the proceedings of the 7th conference on
"Finite Volumes for Complex Applications" (Berlin, June 2014)
covers topics that include 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, as well as the reviewed contributions from
internationally leading researchers in the field of analysis of
finite volume and related methods. Altogether, a rather
comprehensive overview is given 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. Recent
decades have brought significant success 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.
Researchers, PhD and masters level students in numerical
analysis, scientific computing and related fields such as partial
differential equations will find this volume useful, as will
engineers working in numerical modeling and simulations."
General
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