Discrete exterior calculus
Algebraic multigrid for discrete differential forms
Algebraic multigrid for discrete differential forms
Discrete physics using metrized chains
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
PyDEC: Software and Algorithms for Discretization of Exterior Calculus
ACM Transactions on Mathematical Software (TOMS)
Error estimates for generalized barycentric interpolation
Advances in Computational Mathematics
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Mixed finite element methods solve a PDE involving two or more variables. In typical problems from electromagnetics and electrodiffusion, the degrees of freedom associated to the different variables are stored on both primal and dual domain meshes and a discrete Hodge star is used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is essential to the model and numerical stability of a finite element method. We also show how to define interpolation functions and discrete Hodge stars on dual meshes which can be used to create previously unconsidered mixed methods.