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- Runchang Lin, Martin Stynes
- SIAM J. Numerical Analysis
- 2012

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)

- Zhimin Zhang, Runchang Lin, WAYNE STATE
- 2003

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)

- Runchang Lin
- Numerische Mathematik
- 2009

- Zhimin Zhang, Runchang Lin
- Numerische Mathematik
- 2003

The ultraconvergence property of the Zienkiewicz-Zhu gradient patch recovery technique based on local discrete least-squares fitting is established for a large class of even-order finite elements. The result is valid at all rectangular mesh symmetry points. Different smoothing strategies are discussed and numerical examples are demonstrated.

- Runchang Lin, Zhimin Zhang
- SIAM J. Numerical Analysis
- 2008

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)

In [20], we analytically identified natural superconvergent points of function values and gradients for several popular three-dimensional polynomial finite elements via an orthogonal decomposition. This paper focuses on the detailed process for determining the superconvergent points of pentahedral and tetrahedral elements.

- Runchang Lin
- SIAM J. Numerical Analysis
- 2008

- Runchang Lin
- J. Computational Applied Mathematics
- 2016

- Runchang Lin, Zhimin Zhang
- J. Computational Applied Mathematics
- 2012

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)