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Synopsis: One of the currentA?main challenges in the areaA?of scientific computingA? is the design and implementation of accurateA?numerical models forA?complex physical systems which areA?described by time dependent coupled systems of nonlinear PDEs.A?This volume integrates the works of experts in computational mathematics and its applications, with a focusA?on modern algorithms which are at the heart of accurate modeling: adaptive finite element methods, conservative finite difference methods and finite volume methods,A?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.A? A?Researchers and graduate students in A?numerical analysis and numerical solutions of PDEsA?and their scientific computing applications will find this book useful.A