Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider a class of shape optimization problems constrained by nonlocal equations which involve interface–dependent kernels. We derive a novel shape...

Energy piles have recently emerged as a viable alternative to borehole heat exchangers, but their energy efficiency has so far seen little research. In this work, a finite element numerical model is developed for the accurate 3D analysis of transient diffusive and convective heat exchange...

We consider a singularly perturbed boundary value problem with two small parameters. The problem is numerically treated by a quadratic spline collocation method. The suitable choice of collocation points provides the discrete minimum principle. Error bounds for the numerical approximations are...