Fluxes, DG & friends
An interactive, visual course on how computers solve the partial differential equations of heat, flow and transport — from the physical meaning of a flux to discontinuous Galerkin methods, immersed boundaries and GPU kernels. Every figure is a live solver running in your browser.
Who this is for
Students with a computer science background — especially computational geometry and graphics. We assume calculus (derivatives, integrals) and linear algebra (matrices, solving linear systems). Everything else — divergence, weak forms, function spaces, numerical fluxes — is introduced from scratch, with graphics analogies where they help. Hover over dotted terms for a definition.
Chapters
How to use this site
- Read in order the first time: chapters build on each other. The two running examples are the Poisson equation $-\Delta u = f$ (steady heat conduction: an elliptic problem) and conservation laws $\partial_t u + \nabla\cdot \mathbf{F}(u) = 0$ (transport and flow — CFD).
- Play with every widget. The green “Try this” boxes suggest experiments; the orange “What goes wrong” boxes show the classic pitfalls on purpose.
- Everything is verified. The solvers are tested against exact solutions; see the verification appendix, which runs the test suite live.
- Read the code. The source is plain, commented JavaScript with no build step: github.com/VaitkusM/dgfem-applet.