Adaptive finite element analysis of thermal and elasticity problems using Zienkiewicz–Zhu recovery-based error estimation

J. K. Odeyemi; S. A. Odunlami

doi:10.46481/jnsps.2026.3266

Authors

J. K. Odeyemi
[email protected]

Department of Mathematics and Statistics, The Federal Polytechnic Ilaro, Ogun State, Nigeria
S. A. Odunlami
Department of Mechanical Engineering, The Federal Polytechnic Ilaro, Ogun State, Nigeria

Keywords:

Finite element method, Adaptive mesh refinement, Zienkiewicz–Zhu recovery, A posteriori error estimation

Abstract

This paper presents a verification-to-adaptivity analysis of a finite element framework for scalar and vector-valued elliptic problems that employs recovery-based a posteriori error estimation. Conforming bilinear quadrilateral (Q4) and linear triangular (T3) finite elements are used to discretise the thermal Poisson equation and the linear elasticity equations. Standard Galerkin methods are combined with uniform and adaptive mesh refinement in this approach. The approach of manufactured solutions under uniform refinement is first used for verification, where both discretizations regain the theoretical H1- and L2-norm convergence rates, proving the accuracy of the scalar and vector formulations. The Zienkiewicz–Zhu (ZZ) recovery approach is then used to incorporate adaptive refinement, using stress recovery for elasticity and gradient recovery for the thermal problems. The adaptive meshes show conservative effectivity behaviour, monotonic estimator–error correlation, and stable localisation. Differences between Q4 and T3 outcomes are consistent with their known approximation features across all test cases. The findings show that for thermal diffusion and linear elasticity issues, ZZ-driven adaptivity offers a dependable extension of a validated finite element framework.

Dimensions

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