A Conservative Space-time Mesh Refinement Method for the 1-D Wave Equation. Part I: Construction

Summary. We propose a new method for space-time refinement for the 1-D wave equation. This method is based on the conservation of a discrete energy through two different discretization grids which guarantees the stability of the scheme. Our approach results in a non-interpolatory scheme whose stability condition is not affected by the transition between the two grids. Mathematics Subject Classification (1991):65M12