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We propose a methodology to solve high-order PDE boundary value problems with generalised periodicity, in the framework of the C 0 interior penalty method. The method is developed for the analysis of flexoelectricitybased metamaterial unit cells, formalising the corresponding problem statement and weak form, and giving details on the implementation of the local and macro conditions for generalised periodicity. Numerical examples demonstrate the high-order convergence of the method and its applicability in realistic problem settings.

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