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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)
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)
A system of linear coupled reaction-diffusion equations is considered, where each equation is a two-point boundary value problem and all equations share the same small diffusion coefficient. A finite element method using piecewise quadratic splines that are globally C 1 is introduced; its novelty lies in the norm associated with the method, which is(More)