Extras

Cheatsheets

Numerical Recipes. Useful reference that also contains a lot of references to “classical” literature.
Numerical Partial Differential Equations: Finite Difference Methods, by J. W. Thomas. Mostly about FDM (parabolic/hyperbolic equations, stability analysis, matrix methods).
Numerical heat transfer and fluid flow, by Patankar. Covers more advanced CFD (Navier-Stokes, pressure-velocity coupling etc.) topics and has intuitive explanations of the finite volume method.
Numerical Computation of Internal and External Flows: The Fundamentals of Computational Fluid Dynamics, by Hirsh. A comprehensive resource (700-pages) about CFD in particular, not PDE’s in general.
Computational Science and Engineering, by G. Strang (MIT). It develops a framework for the equations and numerical methods of applied mathematics.
Computational methods for Geodynamics, by P. Tackley (ETHZ). CFD, Stokes equations and finite-difference method (with application to convection - Geodynamics).
Introduction to Numerical Geodynamic Modelling, by T. Gerya (ETHZ). Diffusion (heat) and Stokes equations derivation and implementation, finite-differences (with application to thermo-mechanical models - Geodynamics).

any further relevant suggestions are welcome - open a PR

Solving differential equations in parallel on GPUs @JuliaCon2021:
Geo-HPC short course
Advanced GPU Programming with Julia by Sam Omlin (CSCS) and Tim Besard (JuliaComputing) material
Solving differential equations in parallel with Julia @EGU2021
Solving Nonlinear Multi-Physics on GPU Supercomputers with Julia @JuliaCon2021:
Julia for High-Performance Computing by Carsten Bauer at High Performance Computing Center Stuttgart (HLRS)