Titlebook: Numerical Models for Differential Problems; Alfio Quarteroni Textbook 20173rd edition Springer International Publishing, AG 2017 PDE.analy

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Alfio Quarteroniof increasing importance in the analysis and visualization of datasets from a wide variety of scientific domains such as biology, physics, engineering, and medicine. Current challenges of topology-based techniques include the management of time-dependent data, the representation of large and complex

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Alfio Quarteroniomatic search for structures in the data. Of these feature-extraction methods, topological ones stand out due to their solid mathematical foundation. Topologically defined structures—as found in scalar, vector and tensor fields—have proven their merit in a wide range of scientific domains, and scien

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Alfio Quarteronito science and engineering.Includes supplementary material: .When scientists analyze datasets in a search for underlying phenomena, patterns or causal factors, their first step is often an automatic or semi-automatic search for structures in the data. Of these feature-extraction methods, topological

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Generation of 1D and 2D grids,i.e. a partition of the domain in simpler geometric entities (for instance, triangles or quadrangles in two dimensions, tetrahedra, prisms or hexahedra in three dimensions), called the elements, which verify a number of conditions. Similar partitions stand at the base of other approximation methods,

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Elements of finite element programming,tation process can hide some pitfalls. Beyond the syntactic requirements of a given programming language, the need for a high computational efficiency leads to an implementation that is generally not the immediate translation of what has been seen during the theoretical presentation. Efficiency depe

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Discontinuous element methods (DG and mortar),r the spectral element method (Chapter 10). This chapter deals with approximation techniques based on subspaces of polynomials that are discontinuous between elements.We will, in particular, introduce the so-called . method (DG) and the . method. We will carry out this for the Poisson problem first,