Discrete Maximum Principle Based on Repair Technique for Finite Element Scheme of Anisotropic Diffusion Problems (Advances in Applied Mathematics and Mechanics, 2021)
In this paper, we construct a global repair technique for the finite element scheme ofanisotropic diffusion equations to enforce the repaired solutions satisfyingthe discrete maximum principle. It is an extension of the existing localrepair technique. Both of the repair techniquespreserve the total energy and are easy to be implemented. The numericalexperiments show that these repair techniques do not destroy the accuracyof the finite element scheme, and the computational cost of theglobal repair technique is lower than the local repair technique when thediffusion tensors are highly anisotropic.