AI summary · arXiv: 1507.04238v1 · math.NA
On the implementation of the eXtended Finite Element Method (XFEM) for interface problems
The essentials
- The eXtended Finite Element Method (XFEM) is used to solve interface problems with an unfitted mesh
- The authors implemented XFEM in the FEM-library deal.II
- Implementation components include quadrature rule, shape functions, and boundary/interface conditions
- Two exemplary interface problems were solved using the provided code: one with a strong discontinuity and another with a weak discontinuity
- Loss of conformity due to blending effect was discussed for the weak discontinuity case, along with a proposed remedy
- Numerical verification of optimal convergence was conducted to validate the implementation's accuracy in approximating solutions
- This paper contributes to advancing understanding and application of XFEM by providing a detailed implementation in deal.II and demonstrating effectiveness in solving interface problems with discontinuities.
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