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Adaptive Finite Element Methods (AFEM)

Local refinement based on a posteriori error estimates

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Adaptive phase field simulation of fracture propagation.
Adaptive phase field simulation of fracture propagation.
L-shaped Domain
L-shaped domain: Local refinement around corner singularity driven by recovery based (CGL2) error estimator. The colour shows the energy error.

References

Mukesh Kumar, Trond Kvamsdal and Kjetil A. Johannessen: "Simple a posteriori error estimators in adaptive isogeometric analysis", Computers and Mathematics with Applications, 70: 1555-1582, 2015.

Mukesh Kumar, Trond Kvamsdal and Kjetil A. Johannessen: "Superconvergent patch recovery and a posteriori error estimation technique in adaptive isogeometric analysis", Computer Methods in Applied Mechanics and Engineering, 316: 1086-1156, 2017.