핵심 개념
Presenting a stabilizer-free weak Galerkin method for the Ciarlet-Raviart mixed form of the Biharmonic equation on polygonal meshes.
초록
The content introduces a stabilizer-free weak Galerkin method for the Biharmonic equation, discussing its convergence properties and numerical examples. It covers various finite element methods and their applications to solve the equation efficiently.
1. Introduction:
Discusses the Biharmonic equation in bounded polygonal domains.
Variational form and construction of finite element spaces are explored.
2. SFWG Mixed Scheme:
Introduces notations and numerical formulation for stabilizer-free scheme.
3. Well-Posedness:
Defines norms and establishes well-posedness of the numerical scheme.
4. Error Analysis:
Derives error equations using projection operators.
Estimates errors for both primal and dual problems.
5. Error Estimates:
Provides detailed error estimates for both primal and dual problems.
6. Ritz and Neumann Projections:
Introduces projection operators for different boundary conditions.
7. Inquiry into Error Analysis:
Examines error equations, projections, and their implications thoroughly.
통계
The SFWG method simplifies numerical format.
Convergence rates are O(hk) in H1 norm.
Numerical examples support theoretical results.