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.