A Finite Element Method For Modelling Diffusion Over A Curved Surface

Paul Harris

doi:10.1007/978-3-032-04458-7_10

A Finite Element Method For Modelling Diffusion Over A Curved Surface

Paul Harris

Research output: Chapter in Book/Conference proceeding with ISSN or ISBN › Conference contribution with ISSN or ISBN › peer-review

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.

Original language	English
Title of host publication	Integral Methods In Science And Engineering
Subtitle of host publication	Study and Solutions of Mathematical Models
Editors	Christian Constanda, Bardo Bodmann, Paul Harris
Publisher	Birkhäuser
Chapter	10
Pages	151-161
Number of pages	11
Edition	1
ISBN (Electronic)	9783032044587
ISBN (Print)	9783032044570
DOIs	https://doi.org/10.1007/978-3-032-04458-7_10
Publication status	Published - 1 May 2026

Bibliographical note

Publisher Copyright:
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.

Access to Document

10.1007/978-3-032-04458-7_10

Cite this

@inproceedings{236b5d4f71ef445190ec48e133b56731,

title = "A Finite Element Method For Modelling Diffusion Over A Curved Surface",

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.",

author = "Paul Harris",

note = "Publisher Copyright: {\textcopyright} The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.",

year = "2026",

month = may,

day = "1",

doi = "10.1007/978-3-032-04458-7\_10",

language = "English",

isbn = "9783032044570",

pages = "151--161",

editor = "Christian Constanda and Bardo Bodmann and Paul Harris",

booktitle = "Integral Methods In Science And Engineering",

publisher = "Birkh{\"a}user",

edition = "1",

}

A Finite Element Method For Modelling Diffusion Over A Curved Surface. / Harris, Paul.
Integral Methods In Science And Engineering: Study and Solutions of Mathematical Models. ed. / Christian Constanda; Bardo Bodmann; Paul Harris. 1. ed. Birkhäuser, 2026. p. 151-161.

Research output: Chapter in Book/Conference proceeding with ISSN or ISBN › Conference contribution with ISSN or ISBN › peer-review

TY - GEN

T1 - A Finite Element Method For Modelling Diffusion Over A Curved Surface

AU - Harris, Paul

N1 - Publisher Copyright: © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.

PY - 2026/5/1

Y1 - 2026/5/1

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/105043032474

U2 - 10.1007/978-3-032-04458-7_10

DO - 10.1007/978-3-032-04458-7_10

M3 - Conference contribution with ISSN or ISBN

SN - 9783032044570

SP - 151

EP - 161

BT - Integral Methods In Science And Engineering

A2 - Constanda, Christian

A2 - Bodmann, Bardo

A2 - Harris, Paul

PB - Birkhäuser

ER -

A Finite Element Method For Modelling Diffusion Over A Curved Surface

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this