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The chain collocation method: Hydrodynamic flows on curved surfaces: Spectral numerical methods for radial manifold shapes Benjamin J. Gross , Paul J.
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Mixed mimetic spectral element method for Stokes flow: A pointwise divergence-free solution Jasper J. Kreeft , Marc I. Citation Statistics Citations 0 10 20 '07 '10 '13 ' Semantic Scholar estimates that this publication has citations based on the available data.
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Showing of 63 references. Canonical construction of finite elements Ralf Hiptmair Math.
- Mimetic Discretizations of Continuum Mechanics.
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Some realizations of a discrete Hodge operator: Deriving mimetic difference approximations to differential operators using algebraic topology. Los Alamos National Laboratory, unpublished…. A successful discretization method inherits or mimics fundamental properties of PDEs such as topology, conservation, symmetries, positivity structures and maximum principles.
Mimetic Discretizations of Continuum Mechanics
Construction of such a method is made more difficult when the mesh is distorted so that it can conform and adapt to the physical domain and problem solution. The talk is about one such method - the mimetic finite difference MFD method. The MFD method can be applied to solve PDEs with full tensor coefficients on unstructured polygonal and polyhedral meshes.
These meshes may include arbitrary elements: I present a general framework of the MFD method, give examples of discrete gradient, divergence and curl operators on polygonal and polyhedral meshes, and review existing theoretical results including convergence estimates, orthogonal decomposition theorem, etc. I'll show how the MFD framework can be used to derive and analyze new multi-point flux approximation methods. The MFD method has been applied successfully to several applications including diffusion, electromagnetics, acoustics, and gasdynamics.
It was proved that for diffusion problem, the MFD method produces a family of schemes with equivalent properties.