The paper discusses the error estimations for the div least-squares finite element method (div-LSFEM) on elliptic problems. The key highlights and insights are:
The authors present a complete error analysis for div-LSFEM, which improves the current state-of-the-art results.
The error estimations for both the scalar and flux variables are established using dual arguments. In most cases, only an H^(1+ε) regularity is required.
Optimal error estimates are obtained without any higher regularity assumption in many cases, including the common choices of k=m and k+1=m, where k and m are the degrees of the flux and scalar finite element spaces, respectively.
Superconvergence results are derived, showing improved convergence rates for certain projections of the solution.
Numerical experiments are provided to confirm the theoretical analysis.
The authors consider the model problem (1.1) and introduce the first-order system (1.3) to apply the div-LSFEM. The primary error estimates are obtained in Theorem 3.9 using projections. Further superconvergence results are derived in Section 4 by dual arguments.
לשפה אחרת
מתוכן המקור
arxiv.org
תובנות מפתח מזוקקות מ:
by Gang Chen,Fa... ב- arxiv.org 04-09-2024
https://arxiv.org/pdf/2404.04918.pdfשאלות מעמיקות