计算数学有限元方法

the structure of the DG-FEM is very similar to that of the finite element method (FEM), there are several fundamental differences. In particular, the mass matrix is local rather than global and thus can be inverted at very little cost, yielding a semidiscrete scheme that is explicit. Furthermore, by carefully designing the numerical flux to reflect the underlying dynamics, one has more flexibility than in the classic FEM to ensure stability for wavedominated problems. Compared with the FVM, the DG-FEM overcomes the key limitation on achieving high-order accuracy on general grids by enabling this through the local element-based basis

heat.cpp