Supercloseness analysis and polynomial preserving recovery for a class of weak Galerkin methods. (English) Zbl 1390.65150
The authors conduct a supercloseness analysis and polynomial preserving recovery for a class of weak Galerkin (WG) methods. They first present the definition of weak functions and derivatives and present the WG method for the model second order elliptic equation. Later, the authors describe a Lagrange type interpolation operator which is used in the supercloseness analysis. In addition, they present error estimates and the construction of the polynomial preserving recovery operator for WG solutions. Numerical examples are presented to illustrate the discussed theory.
Reviewer: Seenith Sivasundaram (Daytona Beach)
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
Keywords:
second-order elliptic equation; polynomial preserving recovery; supercloseness; superconvergence; weak Galerkin methodReferences:
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