Includes bibliographical references and indexes.

Meshless Finite Element Methods -- Meshless discretisation of nonlocal damage theories -- Three-dimensional non-linear fracture mechanics by enriched meshfree methods without asymptotic enrichment -- Accounting for weak discontinuities and moving boundaries in the context of the Natural Element Method and model reduction techniques -- Discontinuous Galerkin Methods -- Modeling Evolving Discontinuities with Spacetime Discontinuous Galerkin Methods -- Analysis of a finite element formulation for modelling phase separation -- Finite Element Methods with Embedded Discontinuities -- Recent Developments in the Formulation of Finite Elements with Embedded Strong Discontinuities -- Evolving Material Discontinuities: Numerical Modeling by the Continuum Strong Discontinuity Approach (CSDA) -- A 3D Cohesive Investigation on Branching for Brittle Materials -- Partition-of-Unity Based Finite Element Methods -- On Applications of XFEM to Dynamic Fracture and Dislocations -- Some improvements of Xfem for cracked domains -- 2D X-FEM Simulation of Dynamic Brittle Crack Propagation -- A numerical framework to model 3-D fracture in bone tissue with application to failure of the proximal femur -- Application of X-FEM to 3D Real Cracks and Elastic-Plastic Fatigue Crack Growth -- Accurate Simulation of Frictionless and Frictional Cohesive Crack Growth in Quasi-Brittle Materials Using XFEM -- On the Application of Hansbo's Method for Interface Problems -- An optimal explicit time stepping scheme for cracks modeled with X-FEM -- Variational Extended Finite Element Model for Cohesive Cracks: Influence of Integration and Interface Law -- An Evaluation of the Accuracy of Discontinuous Finite Elements in Explicit Dynamic Calculations -- A discrete model for the propagation of discontinuities in a fluid-saturated medium -- Single Domain Quadrature Techniques for Discontinuous and Non-Linear Enrichments in Local Partion of Unity FEM -- Other Discretization Methods -- Numerical determination of crack stress and deformation fields in gradient elastic solids -- The variational formulation of brittle fracture: numerical implementation and extensions -- Measurement and Identification Techniques for Evolving Discontinuities -- Conservation under Incompatibility for Fluid-Solid-Interaction Problems: the NPCL Method.