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Computational fluid dynamics. --- Galerkin methods. --- Sinc-Galerkin methods --- Sinc methods --- Numerical analysis --- CFD (Computational fluid dynamics) --- Fluid dynamics --- Computer simulation --- Data processing

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Differential equations, Elliptic --- Differential equations, Parabolic --- Galerkin methods. --- Numerical solutions. --- 519.63 --- Numerical methods for solution of partial differential equations --- 519.63 Numerical methods for solution of partial differential equations --- Galerkin methods --- Sinc-Galerkin methods --- Sinc methods --- Numerical analysis --- Numerical solutions

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The focus of this monograph is the development of space-time adaptive methods to solve the convection/reaction dominated non-stationary semi-linear advection diffusion reaction (ADR) equations with internal/boundary layers in an accurate and efficient way. After introducing the ADR equations and discontinuous Galerkin discretization, robust residual-based a posteriori error estimators in space and time are derived. The elliptic reconstruction technique is then utilized to derive the a posteriori error bounds for the fully discrete system and to obtain optimal orders of convergence. As coupled surface and subsurface flow over large space and time scales is described by (ADR) equation the methods described in this book are of high importance in many areas of Geosciences including oil and gas recovery, groundwater contamination and sustainable use of groundwater resources, storing greenhouse gases or radioactive waste in the subsurface.

Physical geography. --- Galerkin methods. --- Sinc-Galerkin methods --- Sinc methods --- Numerical analysis --- Numerical analysis. --- Differential equations, partial. --- Numerical Analysis. --- Partial Differential Equations. --- Geophysics/Geodesy. --- Geography --- Partial differential equations --- Mathematical analysis --- Partial differential equations. --- Geophysics. --- Geological physics --- Terrestrial physics --- Earth sciences --- Physics --- Differential equations, Partial.

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This monograph provides a compendium of established and novel error estimation procedures applied in the field of Computational Mechanics. It also includes detailed derivations of these procedures to offer insights into the concepts used to control the errors obtained from employing Galerkin methods in finite and linearized hyperelasticity. The Galerkin methods introduced are considered advanced methods because they remedy certain shortcomings of the well-established finite element method, which is the archetypal Galerkin (mesh-based) method. In particular, this monograph focuses on the systematical derivation of the shape functions used to construct both Galerkin mesh-based and meshfree methods. The mesh-based methods considered are the (conventional) displacement-based, (dual-)mixed, smoothed, and extended finite element methods. In addition, it introduces the element-free Galerkin and reproducing kernel particle methods as representatives of a class of Galerkin meshfree methods. Including illustrative numerical examples relevant to engineering with an emphasis on elastic fracture mechanics problems, this monograph is intended for students, researchers, and practitioners aiming to increase the reliability of their numerical simulations and wanting to better grasp the concepts of Galerkin methods and associated error estimation procedures.

Mechanics. --- Mechanics, Applied. --- Computer mathematics. --- Computational intelligence. --- Solid Mechanics. --- Computational Science and Engineering. --- Computational Intelligence. --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Computer mathematics --- Electronic data processing --- Mathematics --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Galerkin methods. --- Sinc-Galerkin methods --- Sinc methods --- Numerical analysis --- Solids. --- Data processing. --- Solid state physics --- Transparent solids

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This work describes the propagation properties of the so-called symmetric interior penalty discontinuous Galerkin (SIPG) approximations of the 1-d wave equation. This is done by means of linear approximations on uniform meshes. First, a careful Fourier analysis is constructed, highlighting the coexistence of two Fourier spectral branches or spectral diagrams (physical and spurious) related to the two components of the numerical solution (averages and jumps). Efficient filtering mechanisms are also developed by means of techniques previously proved to be appropriate for classical schemes like finite differences or P1-classical finite elements. In particular, the work presents a proof that the uniform observability property is recovered uniformly by considering initial data with null jumps and averages given by a bi-grid filtering algorithm. Finally, the book explains how these results can be extended to other more sophisticated conforming and non-conforming finite element methods, in particular to quadratic finite elements, local discontinuous Galerkin methods and a version of the SIPG method adding penalization on the normal derivatives of the numerical solution at the grid points.  This work is the first publication to contain a rigorous analysis of the discontinuous Galerkin methods for wave control problems. It will be of interest to a range of researchers specializing in wave approximations.

Waves --- Galerkin methods. --- Approximation theory. --- Mathematics. --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Sinc-Galerkin methods --- Sinc methods --- Numerical analysis --- Cycles --- Hydrodynamics --- Benjamin-Feir instability --- Numerical analysis. --- Fourier analysis. --- Differential equations, partial. --- Algorithms. --- Numerical Analysis. --- Fourier Analysis. --- Approximations and Expansions. --- Partial Differential Equations. --- Applications of Mathematics. --- Algorism --- Algebra --- Arithmetic --- Partial differential equations --- Math --- Science --- Analysis, Fourier --- Mathematical analysis --- Foundations --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Engineering --- Engineering analysis --- Mathematics --- Differential equations, Partial.