Development of an error estimator for SBFEM

• Grant number: 25/04755-3
• Support Opportunities: Scholarships abroad - Research
• Start date: August 01, 2025
• End date: January 31, 2026
• Field of knowledge: Engineering - Civil Engineering - Structural Engineering
• Principal Investigator: Philippe Remy Bernard Devloo
• Grantee: Philippe Remy Bernard Devloo
• Host Investigator: Chongmin Song
• Host Institution: Faculdade de Engenharia Civil, Arquitetura e Urbanismo (FEC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Company: Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Mecânica (FEM)
• Institution abroad: University of New South Wales (UNSW), Australia
• Associated research grant: 17/15736-3 - Engineering Research Centre in Reservoir and Production Management, AP.PCPE

Abstract

Error Estimation for the scaled boundary finite element methodIn this research we will develop an error estimator for finite element approximations of elliptic problems using a hybridized version of the continuous element technique. The mathematical basis for this error estimator is an extension of the Prager Synge theorem applied to H1 and hybridized H1 approximations.This error estimator will be applied to the scaled boundary finite element method, allowing to generate hp-adaptive approximations for this techniqueUsing SBFem eigenvectors as enrichment functions for GFEMSBFem approximations are particularly suited to approximate singular solutions, such as those associated with fractures. We will extend the basic principle of SBFem to a scaling line (instead of a scaling center) and expect that the lowest order eigenfunctions will represent normal fracture opening and the two shear stress singular modes. These eigenvectors will then be used as enrichment functions for GFEM. The advantage of this approach is that it will allow to generate enrichment functions for general cases such as cracks between different materials. (AU)