A probabilistic approach to phase-field brittle and ductile fracture with random material and
geometric properties is proposed within this work. In the macroscopic failure mechanics …

In this paper, the one-and two-dimensional stochastic multi-order fractional diffusion-wave
equations are introduced and a collocation procedure based on the shifted Jacobi …

A focused summary of one-and two-dimensional models for linear and nonlinear wave
propagation in fractional media is given. The basic models, which represent fractional …

For the discretization of the integral fractional Laplacian $(-\Delta)^ s $, $0< s< 1$, based on
piecewise linear functions, we present and analyze a reliable weighted residual a posteriori …

This survey hinges on the interplay between regularity and approximation for linear and
quasilinear fractional elliptic problems on Lipschitz domains. For the linear Dirichlet integral …

We consider multilevel decompositions of piecewise constants on simplicial meshes that are
stable in $ H^{-s} $ for $ s\in (0, 1) $. Proofs are given in the case of uniformly and locally …

We propose an operator preconditioner for general elliptic pseudodifferential equations in a
domain\varOmega Ω, where\varOmega Ω is either in R^ n R n or in a Riemannian manifold …

We propose and analyze a robust Bramble-Pasciak-Xu (BPX) preconditioner for the integral
fractional Laplacian of order $ s\in (0, 1) $ on bounded Lipschitz domains. Compared with …

We study optimal design problems where the design corresponds to a coefficient in the
principal part of the state equation. The state equation, in addition, is parameter dependent …

We consider the problem of numerically approximating the solutions to an elliptic partial
differential equation (PDE) for which the boundary conditions are lacking. To alleviate this …