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This book provides a snapshot of the state of the art of the
rapidly evolving field of integration of geometric data in finite
element computations. The contributions to this volume, based on
research presented at the UCL workshop on the topic in January
2016, include three review papers on core topics such as fictitious
domain methods for elasticity, trace finite element methods for
partial differential equations defined on surfaces, and Nitsche's
method for contact problems. Five chapters present original
research articles on related theoretical topics, including Lagrange
multiplier methods, interface problems, bulk-surface coupling, and
approximation of partial differential equations on moving domains.
Finally, two chapters discuss advanced applications such as crack
propagation or flow in fractured poroelastic media. This is the
first volume that provides a comprehensive overview of the field of
unfitted finite element methods, including recent techniques such
as cutFEM, traceFEM, ghost penalty, and augmented Lagrangian
techniques. It is aimed at researchers in applied mathematics,
scientific computing or computational engineering.
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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