A finite element method for local second gradient model using Lagrange multipliers

2020 ◽  
pp. 195-200
Author(s):  
R. Chambon ◽  
D. Caillerie ◽  
T. Matsushima
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Lagrange Multipliers ◽  
Gradient Model ◽  
Second Gradient ◽  
Element Method

A C 0 conforming dg finite element method for biharmonic equations on triangle/tetrahedron

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Xiu Ye ◽  
Shangyou Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Optimal Order ◽  
Biharmonic Equations ◽  
Order Error ◽  
Simple Formulation ◽  
Piecewise Polynomials ◽  
Second Gradient ◽  
Strong Gradient ◽  
Element Method

Abstract A C 0 conforming discontinuous Galerkin (CDG) finite element method is introduced for solving the biharmonic equation. The first strong gradient of C 0 finite element functions is a vector of discontinuous piecewise polynomials. The second gradient is the weak gradient of discontinuous piecewise polynomials. This method, by its name, uses nonconforming (non C 1) approximations and keeps simple formulation of conforming finite element methods without any stabilizers. Optimal order error estimates in both a discrete H 2 norm and the L 2 norm are established for the corresponding finite element solutions. Numerical results are presented to confirm the theory of convergence.

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