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Non-standard finite element methods, in particular mixed methods, are central to many applications. In this text the authors, Boffi, Brezzi and Fortin present a general framework, starting with a finite dimensional presentation, then moving on to formulation in Hilbert spaces and finally considering approximations, including stabilized methods and eigenvalue problems. This book also provides an introduction to standard finite element approximations, followed by the construction of elements for the approximation of mixed formulations in H(div) and H(curl). The general theory is applied to some classical examples: Dirichlet's problem, Stokes' problem,  plate problems, elasticity and electromagnetism.

Engineering mathematics. --- Finite element method. --- Mathematical analysis. --- Mathematics --- Physical Sciences & Mathematics --- Mathematics - General --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Mathematics. --- Computer mathematics. --- Mechanics. --- Mechanics, Applied. --- Computational Mathematics and Numerical Analysis. --- Computational Science and Engineering. --- Theoretical and Applied Mechanics. --- Numerical analysis --- Isogeometric analysis --- Computer science --- Computer science. --- Mechanics, applied. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Informatics --- Science --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Finite element method --- Data processing.

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The book comprises contributions by some of the most respected scientists in the field of mathematical modeling and numerical simulation of the human cardiocirculatory system. It covers a wide range of topics, from the assimilation of clinical data to the development of mathematical and computational models, including with parameters, as well as their efficient numerical solution, and both in-vivo and in-vitro validation. It also considers applications of relevant clinical interest. This book is intended for graduate students and researchers in the field of bioengineering, applied mathematics, computer, computational and data science, and medicine wishing to become involved in the highly fascinating task of modeling the cardiovascular system.

Electrocardiography --- ECG --- EKG --- Electrocardiograms --- Electrodiagnosis --- Heart --- Mathematical models. --- Diseases --- Diagnosis --- Electric properties --- Computer science --- Computer science. --- Biology --- Cardiovascular system. --- Computational Mathematics and Numerical Analysis. --- Math Applications in Computer Science. --- Computer Appl. in Life Sciences. --- Cardiovascular Biology. --- Mathematics. --- Data processing. --- Circulatory system --- Vascular system --- Blood --- Informatics --- Science --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Circulation --- Mathematics --- Computer mathematics. --- Computer science—Mathematics. --- Bioinformatics . --- Computational biology . --- Bioinformatics --- Bio-informatics --- Biological informatics --- Information science --- Computational biology --- Systems biology --- Data processing

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Since the early 70's, mixed finite elements have been the object of a wide and deep study by the mathematical and engineering communities. The fundamental role of this method for many application fields has been worldwide recognized and its use has been introduced in several commercial codes. An important feature of mixed finite elements is the interplay between theory and application. Discretization spaces for mixed schemes require suitable compatibilities, so that simple minded approximations generally do not work and the design of appropriate stabilizations gives rise to challenging mathematical problems. This volume collects the lecture notes of a C.I.M.E. course held in Summer 2006, when some of the most world recognized experts in the field reviewed the rigorous setting of mixed finite elements and revisited it after more than 30 years of practice. Applications, in this volume, range from traditional ones, like fluid-dynamics or elasticity, to more recent and active fields, like electromagnetism.

Differential geometry. Global analysis --- Partial differential equations --- Numerical analysis --- Classical mechanics. Field theory --- Thermodynamics --- Computer. Automation --- differentiaalvergelijkingen --- thermodynamica --- differentiaal geometrie --- algoritmen --- mechanica --- numerieke analyse

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Since the early 70's, mixed finite elements have been the object of a wide and deep study by the mathematical and engineering communities. The fundamental role of this method for many application fields has been worldwide recognized and its use has been introduced in several commercial codes. An important feature of mixed finite elements is the interplay between theory and application. Discretization spaces for mixed schemes require suitable compatibilities, so that simple minded approximations generally do not work and the design of appropriate stabilizations gives rise to challenging mathematical problems. This volume collects the lecture notes of a C.I.M.E. course held in Summer 2006, when some of the most world recognized experts in the field reviewed the rigorous setting of mixed finite elements and revisited it after more than 30 years of practice. Applications, in this volume, range from traditional ones, like fluid-dynamics or elasticity, to more recent and active fields, like electromagnetism.

Finite element method --- Applied Mathematics --- Engineering & Applied Sciences --- Numerical analysis --- Mathematics. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Partial differential equations. --- Numerical analysis. --- Physics. --- Continuum physics. --- Numerical Analysis. --- Partial Differential Equations. --- Numerical and Computational Physics. --- Classical Continuum Physics. --- Global Analysis and Analysis on Manifolds. --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Mathematical analysis --- Partial differential equations --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Math --- Science --- Differential equations, partial. --- Global analysis. --- Numerical and Computational Physics, Simulation. --- Classical and Continuum Physics. --- Global analysis (Mathematics) --- Differential equations, Partial. --- Field theory (Physics) --- Manifolds (Mathematics)