Abstract
The objective is to derive and apply residual-type goal-oriented a posteriori error estimators for the discretization error obtained while approximately evaluating the nonlinear J-integral as a fracture criterion in linear elastic fracture mechanics (LEFM) using the extended finite element method (XFEM). The upper-bound error estimator proposed is based on the solutions of Neumann problems for both the primal and an auxiliary dual problem on the element level for which equilibrated tractions are computed in terms of ansatz functions that are L 2-orthogonal to the XFEM ansatz functions.
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Rüter, M., Stein, E. (2011). Goal-Oriented Residual Error Estimates for XFEM Approximations in LEFM. In: Mueller-Hoeppe, D., Loehnert, S., Reese, S. (eds) Recent Developments and Innovative Applications in Computational Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17484-1_26
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DOI: https://doi.org/10.1007/978-3-642-17484-1_26
Publisher Name: Springer, Berlin, Heidelberg
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