hp finite elements (also called hp finite element methods or hp-FEM for short) are adaptive finite elements that combine refinement strategies that choose smaller elements (h-refinement) and increased order of the element-wise approximation, for example a bigger set of approximation functions as in spectral methods.

References

Mathematical Theory

George Em Karniadakis, Spencer J. Sherwin: Spectral/hp element methods for computational fluid dynamics. 2nd ed. (ZMATH)