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Consider the singularly perturbed linear reaction-diffusion problem −ε 2 Δu + bu = f in Ω ⊂ R d , u = 0 on ∂Ω, where d ≥ 1, the domain Ω is bounded with (when d ≥ 2) Lipschitz-continuous boundary ∂Ω, and the parameter ε satisfies 0 < ε 1. It is argued that for this type of problem, the standard energy norm v → [ε 2 |v| 2 1 + v 2 0 ] 1/2 is too weak a norm(More)
In this work, we analytically identify natural superconvergent points of function values and gradients for triangular elements. Both the Poisson equation and the Laplace equation are discussed for polynomial finite element spaces (with degrees up to 8) under four different mesh patterns. Our results verify computer findings of [2], especially, we confirm(More)
A systematic and analytic process is conducted to identify natural superconvergence points of high degree polynomial C 0 finite elements in a three-dimensional setting. This identification is based upon explicitly constructing an orthogonal decomposition of local finite element spaces. Derivative and function value superconvergence points are investigated(More)