A <i>C</i> <sup>0</sup>-conforming DG finite element method for biharmonic equations on triangle/tetrahedron
Xiu Ye, Shangyou Zhang
Abstract
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.
Topics & Concepts
Biharmonic equationMathematicsFinite element methodPiecewiseTetrahedronDiscontinuous Galerkin methodMathematical analysisNorm (philosophy)Mixed finite element methodExtended finite element methodGeometryBoundary value problemPhysicsPolitical scienceLawThermodynamicsAdvanced Numerical Methods in Computational MathematicsNumerical methods in engineeringElectromagnetic Simulation and Numerical Methods