A C0-conforming DG finite element method for biharmonic equations on triangle/tetrahedron - Ye, Xiu; Zhang, Shangyou (Journal of numerical mathematics, 2022)
A -conforming discontinuous Galerkin (CDG) finite element method is introduced for solving the biharmonic equation. The first strong gradient of 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 ) approximations and keeps simple formulation of conforming finite element methods without any stabilizers. Optimal order error estimates in both a discrete -norm and the -norm are established for the corresponding finite element solutions. Numerical results are presented to confirm the theory of convergence.