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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

  • Raman Kumar and Bhupen Deka EMAIL logo

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 ℝd, d = 2, 3. This WG method is equipped with stable finite elements consisting of usual polynomials of degree k ⩾ 1 for the velocity and polynomials of degree k − 1 for the pressure, both are discontinuous. Optimal convergence rates of order k + 1 for the velocity and order k for the pressure are established in L2-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.

JEL Classification: 65N15; 65N30; 76D07; 35B45; 35J50

Acknowledgement

The authors are grateful to the anonymous referee for valuable comments and suggestions which greatly improved the presentation of this paper.

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Received: 2023-09-01
Revised: 2024-03-26
Accepted: 2024-04-05
Published Online: 2024-04-04
Published in Print: 2024-12-15

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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