Low order nonconforming finite element methods for nuclear reactor model

Abstract

A uniform framework of the linearized fully decoupled fully discrete schemes is developed and investigated with low order nonconforming finite element methods (FEMs) for nuclear reactor model. On the one hand, a general scheme called Scheme I is constructed. Then, the modified Ritz projection and mathematical induction are used to obtain its unconditional optimal error estimate in the L2-norm and superclose estimates in the broken H1-norm, thereby correcting the mistake in previous literature and eliminating the need for the so-called popular time-space splitting method. On the other hand, a new positivity-preserving scheme named Scheme II, which combines the traditional FEMs with cut-off post-processing method, is designed to avoid the non-physical oscillation in numerical calculations. Based on the results of Scheme I, an optimal error estimate in the L2-norm for Scheme II is also derived. Finally, taking the nonconforming EQ1rot element as an example, some numerical experiments are provided to demonstrate the theoretical results. It is worth noting that the analysis presented herein is also suitable for simulating nuclear reactor model in the narrow channel with anisotropic meshes.