A Comparison of Consistent Discretizations for Elliptic Problems on Polyhedral Grids
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Date
2020Metadata
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Original version
Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples: FVCA 9, Bergen, Norway, June 2020. 2020, 585-594. 10.1007/978-3-030-43651-3_55Abstract
In this work, we review a set of consistent discretizations for second-order elliptic equations, and compare and contrast them with respect to accuracy, monotonicity, and factors affecting their computational cost (degrees of freedom, sparsity, and condition numbers). Our comparisons include the linear and nonlinear TPFA method, multipoint flux-approximation (MPFA-O), mimetic methods, and virtual element methods. We focus on incompressible flow and study the effects of deformed cell geometries and anisotropic permeability.