Computer simulation of fracture processes remains a challenge for many industrial modelling problems. In a classical finite element method, the non-smooth displacement near the crack tip is captured by refining the mesh locally. The number of degrees of freedom may drastically increase, especially in three dimensional applications. Moreover, the incremental computation of a crack growth needs f...

Electrical impedance tomography (EIT) is a non-invasive imaging technique where a conductivity distribution in a domain is reconstructed from boundary voltage measurements. The voltage data are generated by injecting currents into the domain. This is an ill-conditioned non-linear inverse problem. Small measurement or forward modeling errors can lead to unbounded fluctuations in the reconstructi...

In this paper, a new high-order multiscale finite element method is developed for elliptic problems with highly oscillating coefficients. The method is inspired by the multiscale finite element method developed in [3], but a more explicit multiscale finite element space is constructed. The approximation space is nonconforming when oversampling technique is used. We use a PetrovGalerkin formulat...

We design an adaptive unfitted finite element method on the Cartesian mesh with hanging nodes. derive hp-reliable and efficient residual type a posteriori error estimate K-meshes. A key ingredient is novel hp-domain inverse which allows us to prove stability of under practical interface resolving conditions also lower bound hp estimate. Numerical examples are included.