On the p-version of FEM in one dimension: The known and unknown features

2014/01/07 by Ivo Babuška, Babuška, Ivo, Harri Hakula +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1401.1483

openalex publication_date 2014/01/07 · openalex created_date 2017/06/23 · openalex updated_date 2026/07/28

Abstract

The paper analyses the convergence of the p-version of the FEM when the solution is piecewise analytic function. It focuses on pointwise convergence of the gradient. It shows that at boundary the rate is different than inside the element and there is a Gibbs phenomenon in the neighborhood of the point where the solution is not analytic. The major result is a conjecture written in the form of a theorem. The conjecture is based on careful numerical computations. The known theoretical results are stated.

Related

• hp-FEM for reaction-diffusion equations II. Robust exponential convergence for multiple length scales in corner domains
• Battling Gibbs Phenomenon: On Finite Element Approximations of Discontinuous Solutions of PDEs
• On the exponent of exponential convergence of the p-version FEM spaces
• A new generalization of the P₁ non-conforming FEM to higher\n polynomial degrees
• On necessary and sufficient conditions for finite element convergence