A scale-independent third-order WENO-Z variant, WENO3-ZES4, preserves third-order accuracy at first-order critical points using nonlinear weights with p=1.
An improved WENO-Z scheme
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Accuracy analysis and optimization of scale-independent third-order WENO-Z scheme with critical-point accuracy preservation
A scale-independent third-order WENO-Z variant, WENO3-ZES4, preserves third-order accuracy at first-order critical points using nonlinear weights with p=1.