References of "Fries, T.-P"
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See detailExtended Finite Element Method
Fries, T.-P.; Zilian, Andreas UL; Moës, N.

in International Journal for Numerical Methods in Engineering (2011), 86(4-5), 403

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See detailA localized mixed-hybrid method for imposing interfacial constraints in the extended finite element method (XFEM)
Zilian, Andreas UL; Fries, T.-P.

in International Journal for Numerical Methods in Engineering (2009), 79(6), 733-752

The paper proposes an approach for the imposition of constraints along moving or fixed immersed interfaces in the context of the extended finite element method. An enriched approximation space enables ... [more ▼]

The paper proposes an approach for the imposition of constraints along moving or fixed immersed interfaces in the context of the extended finite element method. An enriched approximation space enables consistent representation of strong and weak discontinuities in the solution fields along arbitrarily-shaped material interfaces using an unfitted background mesh. The use of Lagrange multipliers or penalty methods is circumvented by a localized mixed hybrid formulation of the model equations. In a defined region in the vicinity of the interface, the original problem is re-stated in its auxiliary formulation. The availability of the auxiliary variable enables the consideration of a variety of interface constraints in the weak form. The contribution discusses the weak imposition of Dirichlet- and Neumann-type interface conditions as well as continuity requirements not fulfilled a priori by the enriched approximation. The properties of the proposed approach applied to two-dimensional linear scalar- and vector-valued elliptic problems are investigated by studying the convergence behavior. © 2009 John Wiley & Sons,Ltd. [less ▲]

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See detailOn time integration in the XFEM
Fries, T.-P.; Zilian, Andreas UL

in International Journal for Numerical Methods in Engineering (2009), 79(1), 69-93

The extended finite element method (XFEM) is often used in applications that involve moving interfaces. Examples are the propagation of cracks or the movement of interfaces in two-phase problems. This ... [more ▼]

The extended finite element method (XFEM) is often used in applications that involve moving interfaces. Examples are the propagation of cracks or the movement of interfaces in two-phase problems. This work focuses on time integration in the XFEM. The performance of the discontinuous Galerkin method in time (space-time finite elements (FEs)) and time-stepping schemes are analyzed by convergence studies for different model problems. It is shown that space-time FE achieve optimal convergence rates. Special care is required for time stepping in the XFEM due to the time dependence of the enrichment functions. In each time step, the enrichment functions have to be evaluated at different time levels. This has important consequences in the quadrature used for the integration of the weak form. A time-stepping scheme that leads to optimal or only slightly sub-optimal convergence rates is systematically constructed in this work. © 2009 John Wiley & Sons, Ltd. [less ▲]

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