An adaptive local mesh refinement method for time-dependent partial differential equations

Abstract We discuss an adaptive local mesh refinement procedure for solving time-dependent initial boundary value problems for vector systems of partial differential equations on rectangular spatial domains. The method identifies and groups regions having large local error indicators into rectangular clusters. The time step and computational cells within clustered rectangles are recursively divided until a prescribed tolerance is satisfied. The refined meshes are properly nested within coarser mesh boundaries; thus, simplifying the prescription of interface conditions at boundaries between fine and coarse meshes. Our method may be used with several numerical solution strategies and error indicators. The meshes may be nonuniform and either stationary or moving. A code based on our refinement procedure is used with a MacCormack finite difference method to solve some examples involving systems of hyperbolic conservation laws.

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