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Semi-Lagrangian schemes have been explored by several authors recently for transport problems, in particular for moving interfaces using the level set method. We incorporate the backward error compensation method de- veloped in our paper from 2003 into semi-Lagrangian schemes with almost the same simplicity and three times the complexity of a first order semi-Lagrangian scheme but with improved order of accuracy. Stability and accuracy results are proved for a constant coefficient linear hyperbolic equation. We apply this technique to the level set method for interface computation.

Back and forth error compensation and correction methods for semi-lagrangian schemes with application to level set interface computations