Convergence of an adaptive mixed finite element method for general second order linear elliptic problems

The convergence of an adaptive mixed finite element method for general second order linear elliptic problems defined on simply connected bounded polygonal domains is analyzed in this paper. The main difficulties in the analysis are posed by the non-symmetric and indefinite form of the problem along with the lack of the orthogonality property in mixed finite element methods. The important tools in the analysis are a posteriori error estimators, quasi-orthogonality property and quasi-discrete reliability established using representation formula for the lowest-order Raviart-Thomas solution in terms of the Crouzeix-Raviart solution of the problem. An adaptive marking in each step for the local refinement is based on the edge residual and volume residual terms of the a posteriori estimator. Numerical experiments confirm the theoretical analysis.Comment: 24 pages, 8 figure

Hardness, tensile and wear behaviour of a nonconventional austenitic stainless steel upon sensitization

The objective of this dissertation is to study the effect of sensitization on the mechanical properties such as hardness and tensile strength of a non-conventional austenitic stainless steel with special emphasis on wear properties. A set of samples has been solution annealed by soaking the steel at 1050°C followed by water quenching. On the other hand, a total of four sets of samples of the steel have been given sensitization treatment by holding at 7500C temperature for different soaking time periods ranging from 1 to 7 hours followed by water quenching. The microstructures of both the solution annealed as well as sensitized samples have been observed by optical microscope. The mechanical testing such as microhardness and macrohardness as well as tensile testing of each specimen has been performed. The wear behaviour of the non-conventional stainless steel is determined by using the ball on plate wear testing machine, with varying loads and sliding distances. It is observed that the height loss due to wear increases with increase in sensitization time, applied load and sliding distance. The hardness and yield strength of the investigated stainless steel sharply decreases with increase in sensitization time, whereas the tensile strength of this steel decreases marginally with sensitization time. It is also observed that the ductility values of the specimens decrease with increase in sensitization time

Detection of High Impedance Faults in Microgrids using Machine Learning

This article presents differential protection of the distribution line connecting a wind farm in a microgrid. Machine Learning (ML) based models are built using differential features extracted from currents at both ends of the line to assist in relaying decisions. Wavelet coefficients obtained after feature selection from an extensive list of features are used to train the classifiers. Internal faults are distinguished from external faults with CT saturation. The internal faults include the high impedance faults (HIFs) which have very low currents and test the dependability of the conventional relays. The faults are simulated in a 5-bus system in PSCAD/EMTDC. The results show that ML-based models can effectively distinguish faults and other transients and help maintain security and dependability of the microgrid operation