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A Finite Element Method For Modelling Diffusion Over A Curved Surface

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  • P. J. Harris

    (The University of Brighton)

Abstract

The well known diffusion equation is used to simulate the spread of a quantity over a flat surface (in 2D) or through space (in 3D). However, the standard diffusion equation cannot be used to model the spread of a quantity over a curved surface such as the surface of an of an object in 3D space. However, if the surface is approximated by a set of flat, triangular elements then the diffusion equation can be applied to each element in terms of local variables and then mapped into the global variables using a relatively simple change of variables. This leads to a diffusion type equation with a different diffusion tensor in each element. This equation can then be solved using a finite element type method.

Suggested Citation

  • P. J. Harris, 2026. "A Finite Element Method For Modelling Diffusion Over A Curved Surface," Springer Books,, Springer.
    • Handle: RePEc:spr:sprchp:978-3-032-04458-7_10
    DOI: 10.1007/978-3-032-04458-7_10
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