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Mimetic scalar products of discrete differential forms. (English) Zbl 1352.65417
Summary: We propose a strategy for the systematic construction of the mimetic inner products on cochain spaces for the numerical approximation of partial differential equations on unstructured polygonal and polyhedral meshes. The mimetic inner products are locally built in a recursive way on each \(k\)-cell and, then, globally assembled. This strategy is similar to the implementation of the finite element methods. The effectiveness of this approach is documented by deriving mimetic discretizations and testing their behavior on a set of problems related to the Maxwell equations.

MSC:
65N06 Finite difference methods for boundary value problems involving PDEs
Software:
Triangle
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