The finite element method with anisotropic mesh grading for elliptic problems in domains with corners and edges

Analytic Regularity for Linear Elliptic Systems in Polygons and Polyhedra

“…In particular, our proof covers the statements formulated in [12, sec. 3], and our results generalize those of [2,8].…”

“…Concerning finite anisotropic regularity, the first partial result is due to Apel-Nicaise [2] for the Laplace-Dirichlet problem; more complete and general statements using spaces M are announced in [12] for the same problem; a proof of anisotropic regularity using distinct, but similar spaces, is provided in [8]. Finally, concerning analytic weighted regularity, prior to the present work, we only find two papers relating to three-dimensional domains: [21] where Guo describes the suitable weighted analytic classes of type B, and [24] where estimates along edges are given for the Laplace-Dirichlet problem.…”

Solving Poisson Problems in Polygonal Domains with Singularity Enriched Physics Informed Neural Networks

“…In the 2D case, there are several classes of traditional numerical solvers based on FEM, including singularity representation based approaches [24,61,13], mesh grading [57,3,2], generalized FEM [26] and adaptive FEM [29], etc. These methods require different amounts of knowledge about the analytic solution.…”

Mesh grading in isogeometric analysis

“…The convergence rates corresponding to graded meshes approach the optimal value. We remark here that the same type of graded meshes have also been used in finite element methods for approximating solutions of elliptic problems in three-dimensional domains with edges, see [6,5,4]. Table 5.…”