Explicit Bound for Quadratic Lagrange Interpolation Constant on Triangular Finite Elements
Provides rigorous error bounds for quadratic interpolation on triangles, which is useful for finite element analysis practitioners needing guaranteed error estimates.
The paper proposes an algorithm to compute explicit upper and lower bounds for the quadratic Lagrange interpolation error constant on triangular finite elements, solving an eigenvalue problem with verified bounds. Numerical tests show the bounds are sharp for various triangle shapes.
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/.