Residual-Based A Posteriori Error Estimates for Symmetric Conforming Mixed Finite Elements for Linear Elasticity Problems

A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems of Dirichlet and mixed boundary conditions are proposed. Stability and efficiency of the estimators are proved. Finally, we provide numerical examples to verify the theoretical results

Distributed Time-Sensitive Task Selection in Mobile Crowdsensing

With the rich set of embedded sensors installed in smartphones and the large number of mobile users, we witness the emergence of many innovative commercial mobile crowdsensing applications that combine the power of mobile technology with crowdsourcing to deliver time-sensitive and location-dependent information to their customers. Motivated by these real-world applications, we consider the task selection problem for heterogeneous users with different initial locations, movement costs, movement speeds, and reputation levels. Computing the social surplus maximization task allocation turns out to be an NP-hard problem. Hence we focus on the distributed case, and propose an asynchronous and distributed task selection (ADTS) algorithm to help the users plan their task selections on their own. We prove the convergence of the algorithm, and further characterize the computation time for users' updates in the algorithm. Simulation results suggest that the ADTS scheme achieves the highest Jain's fairness index and coverage comparing with several benchmark algorithms, while yielding similar user payoff to a greedy centralized benchmark. Finally, we illustrate how mobile users coordinate under the ADTS scheme based on some practical movement time data derived from Google Maps