Dual weighted residual method for laser surface hardening of steel problem

Abstract. The main focus of this article is on the development of Adaptive Finite Element Method (AFEM) for the optimal control problem of laser surface hardening of steel governed by a dynamical system consisting of a semi-linear parabolic equation and an ordinary differential equation using Dual Weighted Residual Method (DWR). A posteriori error estimators using DWR method have been developed when a continuous piecewise linear discretization has been used for the finite element approximation of space variables and a discontinuous Galerkin method has been used for time and control discretizations. Further numerical results obtained are presented are compared with residual method numerical results. Key Words. Laser surface of steel problem, Adaptive finite element methods, Dual weighted residual methods, a posteriori error estimates. 1

A priori error estimates for the optimal control of laser surface hardening of steel

A priori error estimates for the optimal control of laser surface hardening of stee

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

Formation of Aluminum Particles with Shell Morphology during Pressureless Spark Plasma Sintering of Fe-Al Mixtures: Current-Related or Kirkendall Effect?

A need to deeper understand the influence of electric current on the structure and properties of metallic materials consolidated by Spark Plasma Sintering (SPS) stimulates research on inter-particle interactions, bonding and necking processes in low-pressure or pressureless conditions as favoring technique-specific local effects when electric current passes through the underdeveloped inter-particle contacts. Until now, inter-particle interactions during pressureless SPS have been studied mainly for particles of the same material. In this work, we focused on the interactions between particles of dissimilar materials in mixtures of micrometer-sized Fe and Al powders forming porous compacts during pressureless SPS at 500-650 °C. Due to the chemical interaction between Al and Fe, necks of conventional shape did not form between the dissimilar particles. At the early interaction stages, the Al particles acquired shell morphology. It was shown that this morphology change was not related to the influence of electric current but was due to the Kirkendall effect in the Fe-Al system and particle rearrangement in a porous compact. No experimental evidence of melting or melt ejection during pressureless SPS of the Fe-Al mixtures or Fe and Al powders sintered separately was observed. Porous FeAl-based compacts could be obtained from Fe-40at.%Al mixtures by pressureless SPS at 650 °C