This book is devoted to the study of partial differential equation
problems both from the theoretical and numerical points of view.
After presenting modeling aspects, it develops the theoretical
analysis of partial differential equation problems for the three
main classes of partial differential equations: elliptic, parabolic
and hyperbolic. Several numerical approximation methods adapted to
each of these examples are analyzed: finite difference, finite
element and finite volumes methods, and they are illustrated using
numerical simulation results. Although parts of the book are
accessible to Bachelor students in mathematics or engineering, it
is primarily aimed at Masters students in applied mathematics or
computational engineering. The emphasis is on mathematical detail
and rigor for the analysis of both continuous and discrete
problems.
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