Numerical Methods For Conservation Laws From Analysis To Algorithms < 2025 >

While classical finite volume methods (Godunov, TVD, WENO) are covered, the book's heart is Discontinuous Galerkin (DG) and ADER (Arbitrary high-order DERivatives) methods. If you work on CFD, astrophysics, or plasma physics, these are the tools of the 2020s, not the 1990s.

The analysis and algorithms are mostly presented in 1D, with a final chapter extending to 2D on structured grids. There is little on unstructured meshes, mesh adaptation, or parallel (MPI/GPU) implementation—which is where real conservation law codes live today. While classical finite volume methods (Godunov, TVD, WENO)

The chapter on limiting for high-order methods is worth the price alone. Hesthaven clearly explains why standard TVD limiters destroy accuracy at smooth extrema and how to implement more sophisticated approaches (moment limiters, WENO-type limiting for DG). There is little on unstructured meshes, mesh adaptation,

The book includes a companion GitHub repository with a simple MATLAB framework. The pseudocode in the text is explicit enough to translate into C++, Fortran, or Julia without frustration. This is rare—most books give equations, not algorithms . The book includes a companion GitHub repository with