Numerical Computation on Curved Surfaces

Colin B. Macdonald
Department of Mathematics, University of British Columbia, Vancouver

Despite the appearance sometimes given in textbooks, not all differential equations are posed on straight lines and rectangles. This talk will introduce some easy-to-use techniques for computing numerical solutions to partial differential equations (PDEs) posed on curved surfaces and other general domains.
I will show some applications in thin-film flows, reaction-diffusion equations, bulk-surface coupling, point clouds, and image processing.
The talk will also outline how a close encounter with instability improved our understanding and numerical analysis of these methods.