On the monotonicity and discrete maximum principle of the finite difference implementation of C⁰-Q² finite element method

2019/05/15 by Li, Hao, Zhang, Xiangxiong · 1 citation
#65N06 #65N12 #65N30 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1905.06422

Abstract

We show that the fourth order accurate finite difference implementation of continuous finite element method with tensor product of quadratic polynomial basis is monotone thus satisfies the discrete maximum principle for solving a scalar variable coefficient equation -∇⋅(a∇ u)+cu=f under a suitable mesh constraint.

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