Explicit Bound for Quadratic Lagrange Interpolation Constant on Triangular Finite Elements

2016/10/14 by Xuefeng Liu, Liu, Xuefeng, Chun’guang You +1 · 2 citations
Engineering · #Numerical methods in engineering #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics

paper · pdf · doi:10.48550/arxiv.1610.04450

Abstract

For the quadratic Lagrange interpolation function, an algorithm is proposed to provide explicit and verified bound for the interpolation error constant that appears in the interpolation error estimation. The upper bound for the interpolation constant is obtained by solving an eigenvalue problem along with explicit lower bound for its eigenvalues. The lower bound for interpolation constant can be easily obtained by applying the Rayleigh-Ritz method. Numerical computation is performed to demonstrate the sharpness of lower and upper bounds of the interpolation constants over triangles of different shapes. An online computing demo is available at http://www.xfliu.org/onlinelab/.

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• A Two-Stage Finite Element Approach for High-precision Guaranteed Lower Eigenvalue Bounds
• A quasi-interpolation operator yielding fully computable error bounds

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