This chapter presents a modification of the alternating-direction collocation (ADC) procedure designed to achieve enhanced accuracy in the neighborhood of a sharp front. The method achieves high-order accuracy while benefitting from the computational efficiencies inherent in the alternating direction procedure. The chapter reviews the ADC method and builds the enhancement procedure. The enhanced ADC method is applied to an example problem. The chapter considers only rectangular subspaces and describes the enhancement-element procedure.
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