Stability and error estimation for component adaptive grid methods

Component adaptive grid (CAG) methods for solving hyperbolic partial differential equations (PDEs) are discussed in this paper. Applying recent stability results for a class of numerical methods on uniform grids, the convergence of these methods for linear problems on component adaptive grids is established here. Furthermore, the computational error can be estimated on CAGs using these stability results. Using these estimates, the error can be controlled on CAGs. Thus, the solution can be computed efficiently on CAGs within a given error tolerance. Computational results for time dependent linear problems in one and two space dimensions are presented.