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This book gives an introduction to the finite element method as a
general computational method for solving partial differential
equations approximately. Our approach is mathematical in nature
with a strong focus on the underlying mathematical principles, such
as approximation properties of piecewise polynomial spaces, and
variational formulations of partial differential equations, but
with a minimum level of advanced mathematical machinery from
functional analysis and partial differential equations. In
principle, the material should be accessible to students with only
knowledge of calculus of several variables, basic partial
differential equations, and linear algebra, as the necessary
concepts from more advanced analysis are introduced when needed.
Throughout the text we emphasize implementation of the involved
algorithms, and have therefore mixed mathematical theory with
concrete computer code using the numerical software MATLAB is and
its PDE-Toolbox. We have also had the ambition to cover some of the
most important applications of finite elements and the basic finite
element methods developed for those applications, including
diffusion and transport phenomena, solid and fluid mechanics, and
also electromagnetics.
This book gives an introduction to the finite element method as a
general computational method for solving partial differential
equations approximately. Our approach is mathematical in nature
with a strong focus on the underlying mathematical principles, such
as approximation properties of piecewise polynomial spaces, and
variational formulations of partial differential equations, but
with a minimum level of advanced mathematical machinery from
functional analysis and partial differential equations.In
principle, the material should be accessible to students with only
knowledge of calculus of several variables, basic partial
differential equations, and linear algebra, as the necessary
concepts from more advanced analysis are introduced when needed.
Throughout the text we emphasize implementation of the involved
algorithms, and have therefore mixed mathematical theory with
concrete computer code using the numerical software MATLAB is and
its PDE-Toolbox.We have also had the ambition to cover some of the
most important applications of finite elements and the basic finite
element methods developed for those applications, including
diffusion and transport phenomena, solid and fluid mechanics, and
also electromagnetics.
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