Improving the Rate of Convergence of High-Order Finite Elements on Polyhedra I: A Priori Estimates

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ANALYSIS OF THE FINITE ELEMENT METHOD FOR TRANSMISSION/MIXED BOUNDARY VALUE PROBLEMS ON GENERAL POLYGONAL DOMAINS ∗ (2010, methodology): “To account for the pathologies in Ω, we work in weighted Sobolev spaces with weights that depend on a particular vertex a more general setting than the one considered in [17].”
Analysis of a modified Schrödinger operator in 2D: Regularity, index, and FEM (2009, methodology): “The numerical approximation of the solutions of (2) for V = 0 was studied in a very large number of papers, including [3, 4, 8, 11, 12 , 24, 27, 53, 56].”
Interface and mixed boundary value problems on $n$-dimensional polyhedral domains (2010, background): “Any point p ∈ Ω(0) is a vertex of Ω, and p is a true vertex precisely when ωp is not an interval of length π.”
Well-posedness and Regularity for the Elasticity Equation with Mixed Boundary Conditions on Polyhedral Domains and Domains with Cracks (2010, methodology): “” The literature is very vast and we would like to mention [3, 5, 14, 23, 24, 27, 29, 38, 39, 40, 49, 50, 51, 58, 59, 71, 73, 76], which contain results relevant for the elasticity on domains with cracks.”