Convergence results for finite element and finite difference approximation of nonlocal fracture

Abstract

We show apriori convergence of the nonlinear Peridynamic models. The model is shown to be well-posed in Hölder space and Sobolev H^2 space. Finite element approximation using linear conforming elements is shown to converge at the rate h^2 where h is the mesh size. Piecewise constant approximation (finite difference) on a uniform grid is shown to converge at the rate h. We numerically demonstrate the convergence for the Mode-I crack propagation problem. We conclude by discussing future works.

Date
Jul 17, 2019 12:00 AM
Event
ICIAM 2019
Location
Valencia, Spain
Prashant K. Jha
Prashant K. Jha
Research Associate

My research is driven by the application of mathematics and computational science to present-day relevant and challeng- ing problems. Specific areas of interest include mechanics of solids and granular media, computational oncology, and multiscale modeling.