New Diagonal-Norm Summation-by-Parts Operators for the First Derivative with Increased Order of Accuracy
نویسندگان
چکیده
In combination with simultaneous approximation terms, summation-by-parts (SBP) operators provide a flexible and efficient methodology that leads to consistent, conservative, and provably stable high-order discretizations. Traditional diagonal-norm SBP operators with a repeating interior point operator lead to solutions that have a global order of accuracy lower than the order of the interior point operator. A new family of diagonal-norm SBP operators is proposed that retains the order of accuracy of the interior operator. This new family of operators is compared to the traditional approach in the context of the linear convection equation, demonstrating a significant improvement in efficiency.
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