Numerical Methods

Finite Element Approximation of Nonlocal Dynamic Fracture Models
In this work we estimate the convergence rate for time stepping schemes applied to nonlocal dynamic fracture modeling. Here we use the …
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Finite Element Convergence for State-Based Peridynamic Fracture Models
We establish the a priori convergence rate for finite element approximations of a class of nonlocal nonlinear fracture models. We …
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Numerical Convergence of Finite Difference Approximations for State-Based Peridynamic Fracture Models
In this work, we study the finite difference approximation for a class of nonlocal fracture models. The nonlocal model is initially …
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Finite Differences and Finite Elements in Nonlocal Fracture Modeling: A Priori Convergence Rates
In this chapter we present a rigorous convergence analysis of finite difference and finite element approximation of nonlinear nonlocal …
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Well-Posed Nonlinear Nonlocal Fracture Models Associated with Double-Well Potentials
In this chapter, we consider a generic class of bond-based nonlocal nonlinear potentials and formulate the evolution over suitable …
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Numerical Convergence of Nonlinear Nonlocal Continuum Models to Local Elastodynamics
We quantify the numerical error and modeling error associated with replac- ing a nonlinear nonlocal bond-based peridynamic model with a …
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Numerical Analysis of Nonlocal Fracture Models in Holder Space
In this work, we calculate the convergence rate of the finite difference approximation for a class of nonlocal fracture models. We …
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