The paper considers the problem of implementation on graphics processors of numerical integration routines for higher order finite element approximations. The design of suitable GPU kernels is investigated in the context of general purpose integration procedures, as well as particular example applications. The most important characteristic of the problem investigated is the large variation of required processor and memory resources associated with different degrees of approximating polynomials. The questions that we try to answer are whether it is possible to design a single integration kernel for different GPUs and different orders of approximation and what performance can be expected in such a case.

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