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A Second-Order Reconstruction for the Weak Galerkin Finite Element Method of Lowest Order
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DOI：10.1007/s10915-025-03001-0.png)
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Abstract
En 中文
A simple second-order reconstruction is proposed for the weak Galerkin finite element method of lowest order where solutions are approximated using piecewise constants on element interiors and facets. The method is known to possess nice approximation properties, such as satisfying inf-sup condition and achieving optimal-order convergence. But the computed solution converges typically at a first-order rate in both $$L^2$$ and $$H^1$$ norm as the mesh is refined. The proposed reconstruction uses only the values of the weak Galerkin approximation on element facets and ensures continuity at facet barycenters. Its construction is simple, problem-independent, and does not require solving any systems. Its second-order convergence in $$L^2$$ norm is proved for the weak Galerkin approximation of Stokes, Poisson, and linear elasticity problems. A conforming reconstruction is also discussed. The second-order convergence of both reconstructions is verified by numerical results in two and three dimensions.
Keywords:
Weak Galerkin
Reconstruction
Stokes flow
Poisson equation
Linear elasticity
Journal
IF:
3.3
Papers:
655
Citations:
9.6K