This substantial revision of the text Numerical Solution of Partial Differential Equations by the Finite Element Method by C. Johnson is a two volume introduction to the computational solution of differential equations using a unified approach organised around the adaptive finite element method. It presents a synthesis of mathematical modelling, analysis and computation. It provides the student with theoretical and practical tools useful for addressing the basic questions of computational mathematical modelling in science and engineering: How to model physical phenomena using differential equations? What are the properties of solutions of differential equations? How to compute solutions in practice? How to estimate and control the accuracy of computed solutions? The first volume begins by developing the basic issues at an elementary level in the context of a set of model problems in ordinary differential equations. The second volume extends the scope to nonlinear differential equations and systems of equations modelling a variety of phenomena such as reaction-diffusion, fluid flow and many-body dynamics, and reaches the frontiers of research.

Revue de presse

'... the aiFe book is successfully attained, viz. to present a unified approach to computational mathematical modelling based on differential equations combining aspects of mathematics, computation and application.' G. Kirlinger, International Mathematical News

'The book is written in an accessible style and is well suited to serve as a basis for courses in mathematics, science and engineering.' Aslib Book Guide

'This is a well-written and highly readable book that should be useful for advanced undergraduates in Mathematics or for other scientists new to the field.' Mark Baldwin and Pijush Bhattacharyya, Mathematics Today

'... provocative and should be taken seriously by all faculty, not just those in applied mathematics ... the ideas of the text could be used in many courses in analysis and computation ... this book provides a vision of computation and analysis that may become a model for the future.' Mathematics of Computation

' ... an excellent text ... a readable, up-to-date, easily accessible, and mathematically sound introduction to finite element methods ... a clear elucidation of the fundamentals of the finite element method at an elementary level.' Society for Industrial and Applied Mathematics

' ... delightful and illuminating ...' Journal of Fluid Mechanics

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