In this paper, a locally conservative, lowest order staggered discontinuous Galerkin method is developed for the Stokes equations. The proposed method allows rough grids and is based on the partition of the domain into arbitrary shapes of quadrilaterals or polygons, which makes the method highly desirable for practical applications. A priori error analysis covering low regularity is demonstrated. A new postprocessing scheme for the velocity earning faster convergence is constructed. Next, adaptive mesh refinement is highly appreciated on quadrilateral and polygonal meshes since hanging nodes are allowed. Therefore, we propose two guaranteed-type error estimators in L2 error of stress and energy error of the postprocessed velocity, respectively. Numerical experiments confirm our theoretical findings and illustrate the flexibility of the proposed method and accuracy of the guaranteed upper bounds.
|Number of pages||22|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|Publication status||Published - 2019 Mar 1|
Bibliographical noteFunding Information:
This author was supported by NRF-2015R1A5A1009350 and NRF-2016R1A2B4014358.This author was supported by National Institute for Mathematical Sciences (NIMS) grant funded by the Korea government (MSIT) (No. B18310000) and NRF -2017R1D1A1B03035708.
© 2018 Elsevier B.V.
All Science Journal Classification (ASJC) codes
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science Applications