A new family of mixed finite elements in IR3
Numerische Mathematik
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Direct discretization of planar div-curl problems
SIAM Journal on Numerical Analysis
Solving diffusion equations with rough coefficients in rough grids
Journal of Computational Physics
Journal of Computational Physics
Applied Numerical Mathematics
Covolume Solutions of Three-Dimensional Div-Curl Equations
SIAM Journal on Numerical Analysis
Convergence analysis of a covolume scheme for Maxwell's equations in three dimensions
Mathematics of Computation
Communications of the ACM
A tensor artificial viscosity using a mimetic finite difference algorithm
Journal of Computational Physics
The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods
SIAM Journal on Numerical Analysis
Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes
SIAM Journal on Numerical Analysis
A mixed finite volume scheme for anisotropic diffusion problems on any grid
Numerische Mathematik
Higher-order mimetic methods for unstructured meshes
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A residual based error estimator for the Mimetic Finite Difference method
Numerische Mathematik
High-order mimetic finite difference method for diffusion problems on polygonal meshes
Journal of Computational Physics
A Higher-Order Formulation of the Mimetic Finite Difference Method
SIAM Journal on Scientific Computing
A finite volume method for approximating 3D diffusion operators on general meshes
Journal of Computational Physics
Convergence analysis of the high-order mimetic finite difference method
Numerische Mathematik
Convergence Analysis of the Mimetic Finite Difference Method for Elliptic Problems
SIAM Journal on Numerical Analysis
Innovative mimetic discretizations for electromagnetic problems
Journal of Computational and Applied Mathematics
The Discrete Duality Finite Volume Method for Convection-diffusion Problems
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Dynamic modeling of sulfate reducing biofilms
Computers & Mathematics with Applications
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
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
Hi-index | 31.46 |
We extend the mimetic finite difference (MFD) method to the numerical treatment of magnetostatic fields problems in mixed div-curl form for the divergence-free magnetic vector potential. To accomplish this task, we introduce three sets of degrees of freedom that are attached to the vertices, the edges, and the faces of the mesh, and two discrete operators mimicking the curl and the gradient operator of the differential setting. Then, we present the construction of two suitable quadrature rules for the numerical discretization of the domain integrals of the div-curl variational formulation of the magnetostatic equations. This construction is based on an algebraic consistency condition that generalizes the usual construction of the inner products of the MFD method. We also discuss the linear algebraic form of the resulting MFD scheme, its practical implementation, and discuss existence and uniqueness of the numerical solution by generalizing the concept of logically rectangular or cubic meshes by Hyman and Shashkov to the case of unstructured polyhedral meshes. The accuracy of the method is illustrated by solving numerically a set of academic problems and a realistic engineering problem.