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One of the current main challenges in the area of scientific computing_ is the design and implementation of accurate numerical models for complex physical systems which are described by time dependent coupled systems of nonlinear PDEs. This volume integrates the works of experts in computational mathematics and its applications, with a focus on modern algorithms which are at the heart of accurate modeling: adaptive finite element methods, conservative finite difference methods and finite volume methods, and multilevel solution techniques. Fundamental theoretical results are revisited in survey articles and new techniques in numerical analysis are introduced. Applications showcasing the efficiency, reliability and robustness of the algorithms in porous media, structural mechanics and electromagnetism are presented.

Researchers and graduate students in numerical analysis and numerical solutions of PDEs and their scientific computing applications will find this book useful.

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Improving Conservation for First-Order System Least Squares Finite-Element Methods, James Adler, Panayot Vassilevski.- Multiscale Coarsening for Linear Elasticity by Energy Minimization, Heiko Andrae, Marco Buck, Oleg Iliev.- Preconditioners for some matrices of two-by-two block form, with applications, I, Owe Axelsson.- A multigrid algorithm for an elliptic problem with a perturbed boundary condition, Andrea Bonito, Joe Pasciak.- Parallel Unsmoothed Aggregation Algebraic Multigrid Algorithms on GPUs, James Brannick, Yao Chen, Xiaozhe Hu, Ludmil Zikatanov.- Aspects of Guaranteed Error Control in Computational Partial Differential Equations, Carsten Carstensen, Christian Merdon, Johannes Neumann.- A Finite Volume Element Method for a Nonlinear Parabolic Problem, Panagiotis Chatzipantelidis, Victor Ginting.- Multidimensional Sensitivity Analysis of Large-scale Mathematical Models, Ivan Dimov, Rayna Georgieva.- Structures and waves in a nonlinear heat-conducting medium, Stefka Dimova, Milena Dimova, Daniela Vasileva.- Efficient parallel algorithms for unsteady incompressible flows, Jean-Luc Guermond, Peter Minev.- Efficient solvers for some classes of time-periodic eddy current optimal control problems.- Michael Kolmbauer, Ulrich Langer.- Robust Algebraic Multilevel Preconditioners for Anisotropic Problems, Johannes Kraus, Maria Lymbery, Svetozar Margenov.- A weak Galerkin mixed finite element method for biharmonic equations, Lin Mu, Junping Wang, Yanqiu Wang, Xiu Ye.- Domain decomposition scheme for first order evolution equations with nonselfadjoint operators, Petr Vabishchevich, Petr Zakharov.- Spectral coarse spaces in robust two-level methods, Joerg Willems.

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