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In this paper we introduce a new nonlinear reconstruction operator over twodimensional triangularized domains with equilateral triangles. We focus on thelocal definition of the operator. The ideas behind this definition come fromsome basic properties of the Harmonic mean of three positive values. We provesome results regarding the approximation properties of the operator and wecarry out some numerical tests giving evidence of the avoidance of any Gibbseffects.

A nonlinear PPH-type reconstruction based on equilateral triangles