First Steps Towards DEC Poisson Convergence Proofs

Thursday, October 23, 2014 - 4:30pm - 5:00pm
Keller 3-180
Anil Hirani (University of Illinois at Urbana-Champaign)
In the original formulation of Discrete Exterior Calculus (DEC) cochains on primal and circumcentric dual meshes were used. The DEC mixed formulation for Poisson's equation can also be written in a way that is similar to a formulation using lowest order Finite Element Exterior Calculus (FEEC). The difference between the DEC and FEEC formulations is in the mass matrices. Otherwise the structures of the stiffness matrices is identical. From this observation, and using a new (?) interpretation of the DEC mass matrices we point out that for some cases proofs that already exist in the literature may be re-purposed to prove convergence of the mixed DEC formulation for the Poisson problem. This is joint work with Alan Demlow (Texas A&M) and Kaushik Kalyanaraman (UIUC).
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