Runchang Lin

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Consider the singularly perturbed linear reaction-diffusion problem −ε2Δu+ bu = f in Ω ⊂ Rd, u = 0 on ∂Ω, where d ≥ 1, the domain Ω is bounded with (when d ≥ 2) Lipschitzcontinuous 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|v|1+‖v‖0] is too weak a norm to measure adequately(More)
A systematic and analytic process is conducted to identify natural superconvergence points of high degree polynomial C0 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)
Derivative superconvergent points under locally equilateral triangular mesh for both the Poisson and Laplace equations are reported. Our results are conclusive. For the Poisson equation, symmetry points are only superconvergent points for cubic and higher order elements. However, for the Laplace equation, most of superconvergent points are not symmetry(More)