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In the present work, we examine and analyze an hp-version interior penaltydiscontinuous Galerkin finite element method for the numerical approximation ofa steady fluid system on computational meshes consisting of polytopic elementson the boundary. This approach is based on the discontinuous Galerkin method,enriched by arbitrarily shaped elements techniques as has been introduced in[13]. In this framework, and employing extensions of trace, Markov-type, andH1/L2-type inverse estimates to arbitrary element shapes, we examine astationary Stokes fluid system enabling the proof of the inf/sup condition andthe hp- a priori error estimates, while we investigate the optimal convergencerates numerically. This approach recovers and integrates the flexibility andsuperiority of the discontinuous Galerkin methods for fluids whenevergeometrical deformations are taking place by degenerating the edges, facets, ofthe polytopic elements only on the boundary, combined with the efficiency ofthe hp-version techniques based on arbitrarily shaped elements withoutrequiring any mapping from a given reference frame.

hp-version analysis for arbitrarily shaped elements on the boundary discontinuous Galerkin method for Stokes systems