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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...

Introducing the finite element method as a general computational method for solving partial differential equations approximately, this book goes on to cover important applications including diffusion and transport phenomena, solid and fluid mechanics and more.