The arbitrary order mixed mimetic finite difference method for the diffusion equation
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Consiglio Nazionale delle Ricerche (IMATI-CNR), Pavia (Italy); Centro di Simulazione Numerica Avanzata (CeSNA) - IUSS Pavia, Pavia (Italy)
Here, we propose an arbitrary-order accurate mimetic finite difference (MFD) method for the approximation of diffusion problems in mixed form on unstructured polygonal and polyhedral meshes. As usual in the mimetic numerical technology, the method satisfies local consistency and stability conditions, which determines the accuracy and the well-posedness of the resulting approximation. The method also requires the definition of a high-order discrete divergence operator that is the discrete analog of the divergence operator and is acting on the degrees of freedom. The new family of mimetic methods is proved theoretically to be convergent and optimal error estimates for flux and scalar variable are derived from the convergence analysis. A numerical experiment confirms the high-order accuracy of the method in solving diffusion problems with variable diffusion tensor. It is worth mentioning that the approximation of the scalar variable presents a superconvergence effect.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE
- Grant/Contract Number:
- AC52-06NA25396
- OSTI ID:
- 1304825
- Report Number(s):
- LA-UR-15-22806
- Journal Information:
- Mathematical Modelling and Numerical Analysis, Vol. 50, Issue 3; ISSN 0764-583X
- Country of Publication:
- United States
- Language:
- English
Web of Science
The High-Order Mixed Mimetic Finite Difference Method for Time-Dependent Diffusion Problems
|
journal | July 2019 |
Annotations on the virtual element method for second-order elliptic problems | preprint | January 2016 |
A high-order discontinuous Galerkin approach to the elasto-acoustic problem | preprint | January 2018 |
The virtual element method for resistive magnetohydrodynamics | preprint | January 2020 |
Similar Records
A Low Order Mimetic Finite Difference Method for Resistive Magnetohydrodynamics in 2D
Mimetic finite difference method for the stokes problem on polygonal meshes