A Quadratic Finite Volume Method for Parabolic Problems (Advances in Applied Mathematics and Mechanics, 2023)
In this paper, a quadratic finite volume method (FVM) for parabolic problems is studied. We first discretize the spatial variables using a quadratic FVM toobtain a semi-discrete scheme. We then employ the backward Euler method and theCrank-Nicolson method respectively to further disctetize the time vatiable so as toderive two full-discrete schemes. The existence and uniqueness of the semi-discreteand full-discrete FVM solutions are established and their optimal error estimates arederived. Finally, we give numerical examples to illustrate the theoretical results.