A stabilizer free weak Galerkin finite element method with supercloseness of order two
Ahmed Al‐Taweel, Xiaoshen Wang, Xiu Ye, Shangyou Zhang
Abstract
Abstract The weak Galerkin (WG) finite element method is an effective and flexible general numerical technique for solving partial differential equations. A simple WG finite element method is introduced for second‐order elliptic problems. First we have proved that stabilizers are no longer needed for this WG element. Then we have proved the supercloseness of order two for the WG finite element solution. The numerical results confirm the theory.
Topics & Concepts
MathematicsFinite element methodGalerkin methodDiscontinuous Galerkin methodMixed finite element methodSmoothed finite element methodExtended finite element methodOrder (exchange)Mathematical analysishp-FEMPartial differential equationFinite element limit analysisStabilizer (aeronautics)Applied mathematicsElement (criminal law)Boundary knot methodBoundary element methodPhysicsStructural engineeringEconomicsThermodynamicsLawPolitical scienceFinanceEngineeringAdvanced Numerical Methods in Computational MathematicsNumerical methods in engineeringElectromagnetic Simulation and Numerical Methods