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2020•Journal of Physics Conference SeriesOpen access

Error Estimate for Two-Dimensional Coupled Burgers’ Equations By Weak Galerkin Finite Element Method

Hashim Abdul-Khaliq Kashkool, Ahmed Hussein

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Abstract

Abstract A weak Galerkin finite element method (WG-FEM) can be considered a general finite element methods for solving partial differential equations (PDEs) by approximating the differential operators as distributions in weak forms. A weak Galerkin finite element method is used in this work for solving two Dimensional Burgers’ equations in lowest order Raviart-Thomas element RT 0 with polynomails of constant basis. Both the continuous and discrete time WG-FEM are analysed.The optimal order estimates in H 2-error and L 2 –error are obtained. Numerical results are applied to clarify the theoretical analysis.

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Abstract A weak Galerkin finite element method (WG-FEM) can be considered a general finite element methods for solving partial differential equations (PDEs) by approximating the differential operators as distributions in weak forms. A weak Galerkin finite element method is used in this work for solving two Dimensional Burgers’ equations in lowest order Raviart-Thomas element RT 0 with polynomails of constant basis. Both the continuous and discrete time WG-FEM are analysed.The optimal order estimates in H 2-error and L 2 –error are obtained. Numerical results are applied to clarify the theoretical analysis.

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Available abstract

Abstract A weak Galerkin finite element method (WG-FEM) can be considered a general finite element methods for solving partial differential equations (PDEs) by approximating the differential operators as distributions in weak forms. A weak Galerkin finite element method is used in this work for solving two Dimensional Burgers’ equations in lowest order Raviart-Thomas element RT 0 with polynomails of constant basis. Both the continuous and discrete time WG-FEM are analysed.The optimal order estimates in H 2-error and L 2 –error are obtained. Numerical results are applied to clarify the theoretical analysis.

Key concepts: Finite element method, Mathematics, Galerkin method, Discontinuous Galerkin method, Extended finite element method, Mathematical analysis, Partial differential equation, Mixed finite element method

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