CRITICAL ANALYSIS SOBOLEV SPACE, POISSON EQAUTION MULTIGRID ALGORITHM AND SCHWARTZ PRECONDITIONERS BY USING OF APPROXIMATIONS AND THEIR APPLICATION IN FEM

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Published Date: 2025-04-11
Author Name: Dr. Suresh Kumar Sahani, Dr. Kripa Sindhu Prasad, Kameshwar Sahani, Dr. Arun Kumar Chaudhary

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"Critical Analysis of Sobolev Space, Poisson Equation Multigrid Algorithm, and Schwartz Preconditioners Using Approximations and Their Application in FEM" offers an in-depth examination of key mathematical concepts and algorithms used in Finite Element Methods (FEM). The book explores Sobolev spaces and their role in defining weak solutions to partial differential equations, focusing on the challenges of selecting appropriate spaces for various problems. It delves into the Poisson equation and the efficiency of multigrid algorithms in solving such problems, analyzing their strengths and limitations. Additionally, the book discusses the use of Schwartz preconditioners to accelerate iterative solvers, highlighting their application in large-scale FEM problems. Through the analysis of approximations and adaptive techniques, the book provides a comprehensive understanding of these methods and their practical applications in computational engineering and physics.