This paper presents a 2D/3D discrete duality finite volume method for solving heterogeneous and anisotropic elliptic equations on very general unstructured meshes. The scheme is based on the definition of discrete divergence and gradient operators that fulfill a duality property mimicking the Green formula. As a consequence, the discrete problem is proved to be well-posed, symmetric and positive-definite. Standard numerical tests are performed in 2D and 3D and the results are discussed and compared with P1 finite elements ones. At last, the method is used for the resolution of a problem arising in biomathematics: the electrocardiogram simulation on a 2D mesh obtained from segmented medical images.