Advanced Finite Element Concepts
Our group has a strong track record in developing novel finite element concepts such as the Embedded Finite Element Method to model fracture. We have developed mixed finite element methods ensuring the inf-sup condition for multi-physics problems such as coupled Cahn-Hilliard-type flow in elastic media, extended phase-field models for fracture, poroelasticity, topology optimization, or gradient-extended plasticity models and have proposed isogeometric based subdivision methods. Our group was the first to propose peridynamics for modeling biological materials. Early works include an all-electron Kohn-Sham density functional theory using hierarchical finite element spaces and Arbitrary Lagrangian Eulerian finite element methods.
Related References
Lejeune E, Linder C, (2021). “Modeling biological materials with peridynamics,” in Peridynamic Modeling, Numerical Techniques, and Applications, 249-273, Elsevier.
Krischok A, Linder C, (2019). “A generalized inf-sup test for multi-field mixed-variational methods,” Computer Methods in Applied Mechanics and Engineering, 357:112497.
Dortdivanlioglu B, Krischok A, Beirão da Veiga L, Linder C, (2018). “Mixed isogeometric analysis of strongly coupled diffusion in porous materials,” International Journal for Numerical Methods in Engineering, 114:28-46.
Krischok A, Linder C, (2016). “On the enhancement of low-order mixed finite element methods for the large deformation analysis of diffusion in solids,” International Journal of Numerical Methods in Engineering, 106:278-297.
Schauer V, Linder C, (2015). “The reduced basis method in all-electron calculations with finite elements,” Advances in Computational Mathematics, 41:1035-1047.
Linder C, Zhang X, (2013). “A marching cubes based failure surface propagation concept for three-dimensional finite elements with non-planar embedded strong discontinuities of higher order kinematics,” International Journal for Numerical Methods in Engineering, 96:339-372.
Schauer V, Linder C, (2013). “All-electron Kohn-Sham density functional theory on hierarchic finite element spaces,” Journal of Computational Physics, 250:644-664.
Linder C, Raina A, (2013). “A strong discontinuity approach on multiple levels to model solids at failure,” Computer Methods in Applied Mechanics and Engineering, 253:558-583.
Armero F, Linder C, (2009). “Numerical simulation of dynamic fracture using finite elements with embedded discontinuities,” International Journal of Fracture, 160:119-141.
Linder C, Armero F, (2009). “Finite elements with embedded branching,” Finite Elements in Analysis and Design, 45:280-293.
Armero F, Linder C, (2008). “New finite elements with embedded strong discontinuities in the finite deformation range,” Computer Methods in Applied Mechanics and Engineering, 197:3138-3170.
Linder C, Armero F, (2007). “Finite elements with embedded strong discontinuities for the modeling of failure in solids,” International Journal for Numerical Methods in Engineering, 72:1391-1433.