Numerical methods such as boundary element and finite element methods are widely used for the stress analysis in solid mechanics. This study presents boundary element method based on the displacement discontinuity formulation to solve general problems of interaction between hydraulic fracturing and discontinuities. The crack tip element and a higher order boundary displacement collocation techn...

In this paper, we obtain boundary Harnack estimates and comparison theorem for nonnegative solutions to the linearized Monge-Ampère equations under natural assumptions on the domain, Monge-Ampère measures and boundary data. Our results are boundary versions of Caffarelli and Gutiérrez’s interior Harnack inequality for the linearized Monge-Ampère equations. As an application, we obtain sharp upp...

Phase change materials are substances that absorb and release thermal energy during the process of melting and freezing. This characteristic makes phase change material (PCM)  a favourite choice to integrate it in buildings. Stephan problem including melting and solidification in PMC materials is an practical problem in many engineering processes. The position of the moving boundary, its veloci...