## A discontinuous $$hp$$ finite element method for convection-diffusion problems.(English)Zbl 0924.76051

Summary: 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 artifical 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.

### MSC:

 76M10 Finite element methods applied to problems in fluid mechanics 76M25 Other numerical methods (fluid mechanics) (MSC2010) 76R99 Diffusion and convection
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### References:

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