منابع مشابه
Discrete Exterior Calculus
The language of modern mechanics is calculus on manifolds, and exterior calculus is an important part of that. It consists of objects like differential forms, general tensors and vector fields on manifolds, and operators that act on these. While the smooth exterior calculus has a long history going back to Cartan, Lie, Grassmann, Hodge, de Rham and many others, the need for a discrete calculus ...
متن کاملExterior Calculus: Economic Profit Dynamics
A mathematical model for the Dynamics of Economic Profit is constructed by proposing a characteristic differential oneform for this dynamics (analogous to the action in Hamiltonian dynamics). After processing this form with exterior calculus, a pair of characteristic differential equations is generated and solved for the rate of change of profit P as a function of revenue R (t) and cost C (t). ...
متن کاملSmoothed projections in finite element exterior calculus
The development of smoothed projections, constructed by combining the canonical interpolation operators defined from the degrees of freedom with a smoothing operator, has proved to be an effective tool in finite element exterior calculus. The advantage of these operators is that they are L2 bounded projections, and still they commute with the exterior derivative. In the present paper we general...
متن کاملFinite Element Exterior Calculus for Parabolic Problems
In this paper, we consider the extension of the finite element exterior calculus from elliptic problems, in which the Hodge Laplacian is an appropriate model problem, to parabolic problems, for which we take the Hodge heat equation as our model problem. The numerical method we study is a Galerkin method based on a mixed variational formulation and using as subspaces the same spaces of finite el...
متن کاملSpectral Numerical Exterior Calculus Methods for Differential Equations on Radial Manifolds
W e develop exterior calculus approaches for partial differential equations on radial manifolds. We introduce numerical methods that approximate with spectral accuracy the exterior derivative d, Hodge star ?, and their compositions. To achieve discretizations with high precision and symmetry, we develop hyperinterpolation methods based on spherical harmonics and Lebedev quadrature. We perform c...
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ژورنال
عنوان ژورنال: Communications on Pure and Applied Mathematics
سال: 2020
ISSN: 0010-3640,1097-0312
DOI: 10.1002/cpa.21885