Journal of Computational Physics
Local reconstruction of a vector field from its normal components on the faces of grid cells
Journal of Computational Physics
Conservation properties of unstructured staggered mesh schemes
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Scientific Computing
Analysis of an exact fractional step method
Journal of Computational Physics
A moving unstructured staggered mesh method for the simulation of incompressible free-surface flows
Journal of Computational Physics
Higher-order mimetic methods for unstructured meshes
Journal of Computational Physics
Discrete calculus methods for diffusion
Journal of Computational Physics
Discrete Lie Advection of Differential Forms
Foundations of Computational Mathematics
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This paper is a review of a number of mathematical concepts from differential geometry and exterior calculus that are finding increasing application in the numerical solution of partial differential equations. The objective of the paper is to introduce the scientist/ engineer to some of these ideas via a number of concrete examples in 2, 3, and 4 dimensions. The goal is not to explain these ideas with mathematical precision but to present concrete examples and enable a physical intuition of these concepts for those who are not mathematicians. The objective of this paper is to provide enough context so that scientist/engineers can interpret, implement, and understand other works which use these elegant mathematical concepts.