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Proper Orthogonal Decomposition Methods for Partial Differential Equations evaluates the potential applications of POD reduced-order numerical methods in increasing computational efficiency, decreasing calculating load and alleviating the accumulation of truncation error in the computational process. Introduces the foundations of finite-differences, finite-elements and finite-volume-elements. Models of time-dependent PDEs are presented, with detailed numerical procedures, implementation and error analysis. Output numerical data are plotted in graphics and compared using standard traditional methods. These models contain parabolic, hyperbolic and nonlinear systems of PDEs, suitable for the user to learn and adapt methods to their own R&D problems.
"This book details the application of the Proper Orthogonal Decomposition (POD) to instationary problems whose spatial semidiscretization is done either by Finite Difference (FD), Finite Element (FE) or Finite Volume (FV) methods. These three discretization methods correspond to the 3 main chapters of the book." --zbMATH