A Quadratic Finite Volume Method for Parabolic Problems

In this paper, a quadratic finite volume method (FVM) for parabolic problems is studied. We first discretize the spatial variables using a quadratic FVM to obtain a semi-discrete scheme. We then employ the backward Euler method and the Crank-Nicolson method respectively to further disctetize the time vatiable so as to derive two full-discrete schemes. The existence and uniqueness of the semi-discrete and full-discrete FVM solutions are established and their optimal error estimates are derived. Finally, we give numerical examples to illustrate the theoretical results.