A weak Galerkin finite element scheme for the Cahn-Hilliard equation | Zendy

Junping Wang | Zendy; Qilong Zhai | Zendy; Ran Zhang | Zendy; Shangyou Zhang | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

A weak Galerkin finite element scheme for the Cahn-Hilliard equation

Author(s) -

Junping Wang,

Qilong Zhai,

Ran Zhang,

Shangyou Zhang

Publication year - 2018

Publication title -

mathematics of computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.95

H-Index - 103

eISSN - 1088-6842

pISSN - 0025-5718

DOI - 10.1090/mcom/3369

Subject(s) - mathematics , galerkin method , piecewise , finite element method , cahn–hilliard equation , convergence (economics) , scheme (mathematics) , discontinuous galerkin method , mathematical analysis , boundary (topology) , order (exchange) , function (biology) , element (criminal law) , partial differential equation , physics , thermodynamics , finance , evolutionary biology , biology , political science , law , economics , economic growth

This article presents a weak Galerkin (WG) finite element method for the Cahn-Hilliard equation. The WG method makes use of piecewise polynomials as approximating functions, with weakly defined partial derivatives (first and second order) computed locally by using the information in the interior and on the boundary of each element. A stabilizer is constructed and added to the numerical scheme for the purpose of providing certain weak continuities for the approximating function. A mathematical convergence theory is developed for the corresponding numerical solutions, and optimal order of error estimates are derived. Some numerical results are presented to illustrate the efficiency and accuracy of the method.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research