Error analysis of DKT elements for biharmonic equation gives regularity-free first-order convergence bounds via best-approximation and oscillation terms, plus 3D extension and a posteriori estimates.
Quasi-optimal polytopal finite element methods for biharmonic equation
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abstract
This paper establishes quasi-optimal and lower-order error estimates for weak Galerkin, discontinuous Galerkin, and hybrid-high order finite element methods for the biharmonic equation under minimal regularity assumptions on general polytopal meshes. Furthermore, it is shown that the stabilization is an efficient contribution in a~posteriori error estimators.
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2026 1verdicts
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An error analysis of discrete Kirchhoff elements
Error analysis of DKT elements for biharmonic equation gives regularity-free first-order convergence bounds via best-approximation and oscillation terms, plus 3D extension and a posteriori estimates.