Chandra Shekhar Upadhyay

Bio: Chandra Shekhar Upadhyay is an academic researcher from Indian Institute of Technology Kanpur. The author has contributed to research in topics: Finite element method & Spectral element method. The author has an hindex of 19, co-authored 76 publications receiving 1476 citations. Previous affiliations of Chandra Shekhar Upadhyay include Texas A&M University & Indian Institute of Technology, Jodhpur.

Validation of A-Posteriori Error Estimators by Numerical Approach

Abstract: : A numerical methodology which determines the quality (or robustness) of a-posteriori error estimators is described. The methodology accounts precisely for the factors which affect the quality of error estimators for finite-element solutions of linear elliptic problems, namely, the local geometry of the grid and the structure of the solution. The methodology can be employed to check the robustness of any estimator for the complex grids which are used in engineering computations.

A posteriori estimation and adaptive control of the pollution error in the h‐version of the finite element method

Abstract: : We studied the pollution-error in the h-version of the finite element method and its effect on the quality of the local error indicators (resp. the quality of the derivatives recovered by local postprocessing) in the interior of the mesh. Here we show that it is possible to construct a-posteriori estimates of the pollution-error in a patch of elements by employing the local error indicators over the entire mesh. We also give an adaptive algorithm for the local control of the pollution-error in a patch of elements of interest.

A Posteriori Error Estimation in Finite Element Analysis

Abstract: This monograph presents a summary account of the subject of a posteriori error estimation for finite element approximations of problems in mechanics. The study primarily focuses on methods for linear elliptic boundary value problems. However, error estimation for unsymmetrical systems, nonlinear problems, including the Navier-Stokes equations, and indefinite problems, such as represented by the Stokes problem are included. The main thrust is to obtain error estimators for the error measured in the energy norm, but techniques for other norms are also discussed.

Quantification of uncertainty in computational fluid dynamics

Abstract: This review covers Verification, Validation, Confirmation and related subjects for computational fluid dynamics (CFD), including error taxonomies, error estimation and banding, convergence rates, surrogate estimators, nonlinear dynamics, and error estimation for grid adaptation vs Quantification of Uncertainty.

Verification and Validation in Scientific Computing

Abstract: Advances in scientific computing have made modelling and simulation an important part of the decision-making process in engineering, science, and public policy. This book provides a comprehensive and systematic development of the basic concepts, principles, and procedures for verification and validation of models and simulations. The emphasis is placed on models that are described by partial differential and integral equations and the simulations that result from their numerical solution. The methods described can be applied to a wide range of technical fields, from the physical sciences, engineering and technology and industry, through to environmental regulations and safety, product and plant safety, financial investing, and governmental regulations. This book will be genuinely welcomed by researchers, practitioners, and decision makers in a broad range of fields, who seek to improve the credibility and reliability of simulation results. It will also be appropriate either for university courses or for independent study.