Numerical smoothness and error analysis for RKDG on the scalar nonlinear conservation laws
Tong Sun, David Rumsey
TL;DR
This paper introduces a new concept of numerical smoothness to derive an a posteriori error estimate for high-order RKDG methods solving scalar nonlinear conservation laws, focusing on smooth solutions.
Contribution
It develops an error analysis framework based on numerical smoothness, providing optimal convergence rates for RKDG methods of arbitrary order on smooth solutions.
Findings
Established an a posteriori error estimate with optimal convergence rate.
Focused on smooth solutions, setting groundwork for future discontinuous solution analysis.
Applied the concept of numerical smoothness to error analysis in RKDG methods.
Abstract
The new concept of numerical smoothness is applied to RKDG methods on the scalar nonlinear conservation laws. The main result is an a posteriori error estimate for the RKDG methods of arbitrary order in space and time, with optimal convergence rate. In this paper, the case of smooth solutions is the focus point. However, the error analysis framework is prepared to deal with discontinuous solutions in the future.
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Taxonomy
TopicsComputational Fluid Dynamics and Aerodynamics · Advanced Numerical Methods in Computational Mathematics · Meteorological Phenomena and Simulations