Implicit solution of hyerbolic equations with space-time adaptivity
The authors use the finite volume method in space and a linear multistep method in time on a structured grid to solve numerically multidimensional scalar hyperbolic differential equations in conservation form. The convergence of the numerical solution to the weak solution as volume and time step go to zero has been proved and the corresponding iteration method is discussed. The adaptive algorithm is implemented for parallel execution and the test numerical results are presented for linear problems and compressible Euler equations. In all cases the algorithm selects a grid and a time step adapted to the solutions of the equations.
multidimensional hyperbolic conservation law
scientific article; zbMATH DE number 1749888