Аннотация
This paper presents a new method which exhibits the best features
of both finite volume and finite element techniques. Special attention
is given to the issues of conservation, flexible accuracy, and stability.
The method is elementwise conservative, the order of polynomial approximation
can be adjusted element by element, and the stability is not based
on the introduction of artificial diffusion, but on the use of a
very particular finite element formulation with discontinuous basis
functions. The method supports h-, p-, and hp-approximations and
can be applied to any type of meshes, including non-matching grids.
A priori error estimates and numerical experiments on representative
model problems indicate that the method is robust and capable of
delivering high accuracy.
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