  A family of quadratic finite volume method (FVM) schemes are constructed and
analyzed over tetrahedral meshes. In order to prove stability and error
estimate, we propose the minimum V-angle condition on tetrahedral meshes, and
the surface and volume orthogonal conditions on dual meshes. Through the
element analysis technique, the local stability is equivalent to a positive
definiteness of a $9\times9$ element matrix, which is difficult to analyze
directly or even numerically. With the help of the surface orthogonal condition
and congruent transformation, this element matrix is reduced into a block
diagonal matrix, then we carry out the stability result under the minimum
V-angle condition. It is worth mentioning that the minimum V-angle condition of
the tetrahedral case is very different from a simple extension of the minimum
angle condition for triangular meshes, while it is also convenient to use in
practice. Based on the stability, we prove the optimal $ H^{1} $ and $L^2$
error estimates respectively, where the orthogonal conditions play an important
role in ensuring optimal $L^2$ convergence rate. Numerical experiments are
presented to illustrate our theoretical results.
