Additional grid points are often introduced for the higher-order polynomial of a numerical solution with curvilinear elements. However, those points are likely to be located slightly outside the domain, even when the vertices of the curvilinear elements lie within the curved domain. This misallocation of grid points generates a mesh error, called geometric approximation error. This error is smaller than the discretization error but large enough to significantly degrade a long-time integration. Moreover, this mesh error is considered to be the leading cause of conservation error. Two novel schemes are proposed to improve conservation error and/or discretization error for long-time integration caused by geometric approximation error: The first scheme retrieves the original divergence of the original domain; the second scheme reconstructs the original path of differentiation, called connection, thus retrieving the original connection. The increased accuracies of the proposed schemes are demonstrated by the conservation error for various partial differential equations with moving frames on the sphere.
|Journal||Journal of Scientific Computing|
|Publication status||Published - 2022 Jul|
Bibliographical noteFunding Information:
This research was supported by the National Research Foundation of Korea (NRF-2021R1A2C109297811). The second author is supported by the R &D project “Development of a Next-generation Operational System by the Korea Institute of Atmospheric Prediction Systems (KIAPS)”, funded by the Korea Meteorological Administration (KMA2020-02213).
© 2022, The Author(s).
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Numerical Analysis
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics