Weak Galerkin finite element method for solving one-dimensional coupled Burgers’ equations

Abstract

In this paper, we apply a weak Galerkin method for solving one dimensional coupled Burgers’ equations. Based on a conservation form for nonlinear term and some of the technical derivational. Theorticly, we drive the optimal order error in \(L^2\) and \(H^1\) norm for both continuous and discrete time weak Galerkin finite element schemes, also the stability of continuous time weak Galerkin finite element method is proved. Numerically, the accuracy and effectiveness of the weak Galerkin finite element method are illustrated by using Numerical examples with the lower order Raviart–Thomas element \(RT_k\) for discrete weak derivative space.

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Correspondence to Ahmed J. Hussein.

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Hussein, A.J., Kashkool, H.A. Weak Galerkin finite element method for solving one-dimensional coupled Burgers’ equations. J. Appl. Math. Comput. 63, 265–293 (2020). https://doi.org/10.1007/s12190-020-01317-8

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Keywords

  • Weak Galerkin finite element method (WG-FEM)
  • Burgers’ equations
  • Optimal order

Mathematics Subject Classification

  • 65N15
  • 65N30