The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes
Journal of Computational Physics
Journal of Computational Physics
The Discrete Duality Finite Volume Method for Convection-diffusion Problems
SIAM Journal on Numerical Analysis
Error Analysis for a Mimetic Discretization of the Steady Stokes Problem on Polyhedral Meshes
SIAM Journal on Numerical Analysis
A Mimetic Discretization of the Stokes Problem with Selected Edge Bubbles
SIAM Journal on Scientific Computing
Arbitrary-Order Nodal Mimetic Discretizations of Elliptic Problems on Polygonal Meshes
SIAM Journal on Numerical Analysis
Mimetic Discretizations of Elliptic Control Problems
Journal of Scientific Computing
Equivalent projectors for virtual element methods
Computers & Mathematics with Applications
Numerical results for mimetic discretization of Reissner---Mindlin plate problems
Calcolo: a quarterly on numerical analysis and theory of computation
Mimetic finite difference method
Journal of Computational Physics
Mimetic scalar products of discrete differential forms
Journal of Computational Physics
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We propose a family of mimetic discretization schemes for elliptic problems including convection and reaction terms. Our approach is an extension of the mimetic methodology for purely diffusive problems on unstructured polygonal and polyhedral meshes. The a priori error analysis relies on the connection between the mimetic formulation and the lowest order Raviart-Thomas mixed finite element method. The theoretical results are confirmed by numerical experiments.