摘要
.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.
基金
supported in part by the National Natural Science Foundation of China under grant No.11901506
by the Shandong Province Natural Science Foundation under grant No.ZR2018QA003 and ZR2021MA010.