A PDE-constrained optimization formulation for discrete fracture network flows

We investigate a new numerical approach for the computation of the 3D flow in a discrete fracture network that does not require a conforming discretization of partial differential equations on complex 3D systems of planar fractures. The discretization within each fracture is performed independently of the discretization of the other fractures and of their intersections. Independent meshing process within each fracture is a very important issue for practical large scale simulations making easier mesh generation. Some numerical simulations are given to show the viability of the method. The resulting approach can be naturally parallelized for dealing with systems with a huge number of fractures

Where smart meets sustainability: The role of Smart Governance in achieving the Sustainable Development Goals in cities

Sustainable Development Goals (SDGs) seek to achieve economic, social, and environmental progress globally. However, trade-offs among these three pillars might occur, particularly in the context of cities. We argue that these trade-offs exist because the traditional factors of production for economic welfare are not always relevant to the other dimensions of city sustainability. Consequently, additional factors are needed to facilitate the progress of the 2030 agenda. We make a case for smart governance, a factor that we associate with the quality of governance. We explore these ideas by examining the economic, social, and environmental dimensions of 128 cities worldwide. Our results indicate that the traditional factors of production (labor, land, and capital) are positively associated with the economic dimension but weakly associated with the social and environmental dimensions. However, smart governance is positively associated with the various dimensions of urban sustainability

Anisotropic a posteriori error estimate for the virtual element method

We derive an anisotropic a posteriori error estimate for the adaptive conforming virtual element approximation of a paradigmatic two-dimensional elliptic problem. In particular, we introduce a quasi-interpolant operator and exploit its approximation results to prove the reliability of the error indicator. We design and implement the corresponding adaptive polygonal anisotropic algorithm. Several numerical tests assess the superiority of the proposed algorithm in comparison with standard polygonal isotropic mesh refinement schemes

hp-adaptive two-grid discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows

We develop the a posteriori error analysis, with respect to a mesh-dependent energy norm, of two-grid hp-version discontinuous Galerkin finite element methods for quasi-Newtonian flows. The performance of the proposed estimators within an hp-adaptive refinement procedure is studied through a numerical experiment