Question

Quadratic interpolation results in conservation problems. Why?

(a) Their physical problem is non-conservative

(b) They involve quadratic equations

(c) They are higher order schemes

(d) Interpolation curves vary at the face

This question was posed to me in an interview.

This is a very interesting question from Discretization Aspects topic in division Basic Aspects of Discretization, Grid Generation with Appropriate Transformation of Computational Fluid Dynamics

Answer 1

The correct choice is (d) Interpolation curves vary at the face

Best explanation: Quadratic interpolation models the physical problems using quadratic equations. At the intersection faces, we get two different quadratic equations and their values do not cancel out there. This gives a problem to conservation in the Quadratic interpolation schemes.