Surfaces over Dirichlet Tessellations
Computer Aided Geometric Design
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
Error estimates for generalized barycentric interpolation
Advances in Computational Mathematics
PyDEC: Software and Algorithms for Discretization of Exterior Calculus
ACM Transactions on Mathematical Software (TOMS)
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Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is essential to the numerical stability of the method. Additionally, we define interpolation functions and discrete Hodge stars on dual meshes which can be used to create previously unconsidered mixed methods. Examples from magnetostatics and Darcy flow are examined in detail.