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Four-order superconvergent CDG finite elements for the biharmonic equation on triangular meshes.
- Source :
-
Journal of Computational & Applied Mathematics . Apr2024, Vol. 440, pN.PAG-N.PAG. 1p. - Publication Year :
- 2024
-
Abstract
- In a conforming discontinuous Galerkin (CDG) finite element method, discontinuous P k polynomials are employed. To connect discontinuous functions, the inter-element traces, { u h } and { ∇ u h } , are usually defined as some averages in discontinuous Galerkin finite element methods. But in this CDG finite element method, they are defined as projections of a lifted P k + 4 polynomial from four P k polynomials on neighboring triangles. With properly chosen weak Hessian spaces, when tested by discontinuous polynomials, the variation form can have no inter-element integral, neither any stabilizer. That is, the bilinear form is the same as that of conforming finite elements for solving the biharmonic equation. Such a conforming discontinuous Galerkin finite element method converges four orders above the optimal order, i.e., the P k solution has an O (h k + 5) convergence in L 2 -norm, and an O (h k + 3) convergence in H 2 -norm. A local post-process is defined, which lifts the P k solution to a P k + 4 quasi-optimal solution. Numerical tests are provided, confirming the theory. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03770427
- Volume :
- 440
- Database :
- Academic Search Index
- Journal :
- Journal of Computational & Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 173965916
- Full Text :
- https://doi.org/10.1016/j.cam.2023.115516