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Analysis and Computation of a Weak Galerkin Scheme for Solving the 2D/3D Stationary Stokes Interface Problems with High-Order Elements.
- Source :
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Journal of Numerical Mathematics . Apr2024, p1. 29p. - Publication Year :
- 2024
-
Abstract
- In this paper, we present a high-order weak Galerkin finite element method (WG-FEM) for solving the stationary Stokes interface problems with discontinuous velocity and pressure in ℝ<italic>d</italic> (<italic>d</italic> = 2, 3). This WG method is equipped with stable finite elements consisting of usual polynomials of degree <italic>k</italic> ≥ 1 for the velocity and polynomials of degree <italic>k</italic> – 1 for the pressure, both are discontinuous. Optimal convergence rates of order <italic>k</italic> + 1 for the velocity and order <italic>k</italic> for the pressure are established in <italic>L</italic>2-norm on hybrid meshes. Numerical experiments verify the expected order of accuracy for both two-dimensional and three-dimensional examples. Moreover, numerically it is shown that the proposed WG algorithm is able to accommodate geometrically complicated and very irregular interfaces having sharp edges, cusps, and tips. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15702820
- Database :
- Academic Search Index
- Journal :
- Journal of Numerical Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 176402867
- Full Text :
- https://doi.org/10.1515/jnma-2023-0112