In the numerical discretization of partial differential equations (PDEs) with moving frames on curved surfaces, the discretization error does not converge for a high p≥5. Moreover, the conservation error remains significant even in a refined mesh and does not converge as the polynomial order p increases. We postulate that the inaccurate location of the internal grid points of curved elements causes this problem; this is called the internal point error. This bottleneck of convergence persists even when the vertices of the elements are located exactly on the curved domain. We first theoretically explain the effects of the internal point error on numerical accuracy. We then computationally validate the postulation by using a high-order mesh with a negligible internal point error, even for a high-order polynomial of order p. For computational validations, four differential operators and four PDEs are numerically solved using moving frames on the unit sphere to demonstrate the effect of the internal point error.
|Journal||Computer Methods in Applied Mechanics and Engineering|
|Publication status||Published - 2022 Aug 1|
Bibliographical noteFunding Information:
The research of the first author was supported by the National Research Foundation of Korea ( NRF-2021R1A2C109297811 ).
© 2022 The Author(s)
All Science Journal Classification (ASJC) codes
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science Applications