On the monotonicity and discrete maximum principle of the finite difference implementation of $C^0$-$Q^2$ finite element method
arXiv:1905.0642229 citations
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Provides theoretical guarantees for a high-order numerical method, benefiting computational scientists solving elliptic PDEs.
The paper proves that a fourth-order accurate finite difference implementation of the C0-Q2 finite element method is monotone and satisfies the discrete maximum principle for variable-coefficient elliptic equations under a mesh constraint.
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 $-\nabla\cdot(a\nabla u)+cu=f$ under a suitable mesh constraint.