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A Comparison of Consistent Discretizations for Elliptic Problems on Polyhedral Grids

A Comparison of Consistent Discretizations for Elliptic Problems on Polyhedral Grids

Category
Academic chapter/article/Conference paper
Abstract
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.
Client
  • VISTA / 6366
  • Research Council of Norway (RCN) / 244361
Language
English
Affiliation
  • SINTEF Digital / Mathematics and Cybernetics
Year
Publisher
Springer
Book
Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples
Issue
323
ISBN
978-3-030-43650-6
Page(s)
585 - 594