A Finite Element Method For Modelling Diffusion Over A Curved Surface

P. J. Harris ()
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P. J. Harris: The University of Brighton

Chapter Chapter 10 in Integral Methods in Science and Engineering, 2026, pp 151-161 from Springer

Abstract: 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.

Date: 2026
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DOI: 10.1007/978-3-032-04458-7_10

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