- Article
24 Pages
This study proposes a non-uniform meshing strategy for finite element (FE) discretization aimed at improving mechanical accuracy under controlled nodal budgets in structural analyses with localized field gradients. Unlike quasi-uniform meshing, the proposed approach uses a priori node placement based on the zeros of Chebyshev polynomials. Their natural clustering near the endpoints of [−1, 1] is mapped onto the physical domain to generate a non-uniform distribution by construction, without adaptive refinement or iterative remeshing. The main contribution therefore lies not in the Chebyshev points themselves, but in their use as a deterministic, solution-independent rule for placing the vertices of low-order FE meshes. Three meshing strategies are compared: quasi-uniform, graded, and Chebyshev-based meshes. The graded mesh deliberately concentrates nodes in predefined critical regions, whereas the Chebyshev-based mesh follows a predefined analytical placement rule. Performance is assessed against converged fine-mesh FE reference solutions using relative errors in displacement and von Mises stress, local and peak-stress errors, mesh-quality indicators, stiffness-matrix conditioning, and computational cost. For the two-hole plate at the relative displacement error decreases from for the quasi-uniform mesh to for the Chebyshev-based mesh, while the graded mesh reaches Overall, the Chebyshev-based strategy improves displacement accuracy relative to quasi-uniform meshing in the investigated configurations, although the geometrically graded mesh generally achieves lower errors and improvements in stress accuracy are not systematic.
Computation
5 November 2026



![To demonstrate the capabilities of emergent computations, several important observed computational emergent systems are reviewed. Two examples show (a) a manually designed emergent system: logic-gate OR with the input of 11 giving output 1 that is highly prone to insertion of any error (see details in [1]), and (b) a self-organizing, two-level emergent system: ships breading ships: a two-level emergent system that self-organizes itself, mildly resilient to errors (see animations in [1]).](https://mdpi-res.com/computation/computation-14-00276/article_deploy/html/images/computation-14-00276-g001-550.jpg)

