Adaptive biorthogonal spline schemes for advection-reaction equations
Journal of Computational Physics
Solving convection-diffusion-reaction equation by adaptive finite volume element method
Mathematics and Computers in Simulation
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We combine an Eulerian--Lagrangian approach and multiresolution analysis to develop unconditionally stable, explicit, multilevel methods for multidimensional linear hyperbolic equations. The derived schemes generate accurate numerical solutions even if large time steps are used. Furthermore, these schemes have the capability of carrying out adaptive compression without introducing mass balance error. Computational results are presented to show the strong potential of the numerical methods developed.