Improvement of the superconvergent patch recovery technique by the use of constraint equations: the SPR-C technique

• Published in: International journal for numerical methods in engineering Vol. 70; no. 6; pp. 705 - 727
• Main Authors: Ródenas, J. J., Tur, M., Fuenmayor, F. J., Vercher, A.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 07-05-2007; Wiley
• Subjects: adaptivity; Computational techniques; error estimation; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Mathematical methods in physics; Physics; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; superconvergent patch recovery; Finite element method; adaptivity; Error estimation; Polynomial interpolation; Equilibrium equation; Modeling; Numerical convergence; Exact solution; superconvergent patch recovery
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.1903

The superconvergent patch recovery (SPR) technique is widely used in the evaluation of a recovered stress field σ* from the finite element solution σfe. Several modifications of the original SPR technique have been proposed. A new improvement of the SPR technique, called SPR‐C technique (Constrained SPR), is presented in this paper. This new technique proposes the use of the appropriate constraint equations in order to obtain stress interpolation polynomials in the patch σ p* that locally satisfy the equations that should be satisfied by the exact solution. As a result the evaluated expressions for σ p* will satisfy the internal equilibrium and compatibility equations in the whole patch and the boundary equilibrium equation at least in vertex boundary nodes and, under certain circumstances, along the whole boundary of the patch coinciding with the boundary of the domain. The results show that the use of this technique considerably improves the accuracy of the recovered stress field σ* and therefore the local effectivity of the ZZ error estimator. Copyright © 2006 John Wiley & Sons, Ltd.