A monotone $Q^1$ finite element method for anisotropic elliptic equations

Published 25 Oct 2023 in math.NA and cs.NA | (2310.16274v2)

Abstract: We construct a monotone continuous $Q^1$ finite element method on the uniform mesh for the anisotropic diffusion problem with a diagonally dominant diffusion coefficient matrix. The monotonicity implies the discrete maximum principle. Convergence of the new scheme is rigorously proven. On quadrilateral meshes, the matrix coefficient conditions translate into specific mesh constraints.

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