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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.
Introduction.- Newtonian and Eshelbian Mechanics.- Boundary Value Problems.- Galerkin Methods.- Numerical Integration.- Energy Norm A Posteriori Error Estimates.- Goal-oriented A Posteriori Error Estimates in Linearized Elasticity.- Goal-oriented A Posteriori Error Estimates in Finite Hyperelasticity.- Numerical Examples.- The Nonstandard Dyadic Product Operators.- Push-forward and Pull-back Operations.- Tensor derivatives.- A Generalized Nitsche Method.- The J-integral in Elastic FractureMechanics.- Linearizations.- Materials investigated in this monograph.- Functional Analysis—A Synopsis.