Titlebook: Error Estimates for Advanced Galerkin Methods; Marcus Olavi Rüter Book 2019 Springer Nature Switzerland AG 2019 Elastic Fracture Mechanics

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Energy Norm A Posteriori Error Estimates, kernel particle methods. For the time being, we restrict our considerations to the linearized elasticity problem (3.28) because this linear problem allows for the development of verification strategies in a more convenient way. Verification strategies applied to the finite hyperelasticity problem will be detailed in Chap.?8.

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Boundary Value Problems,ary value problems of compressible and (nearly) incompressible finite hyperelasticity within both Newtonian and Eshelbian mechanics. The derivations are performed in terms of their strong and weak forms and supplemented by appropriate linearizations that are used within the iterative Newton-Raphson

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Galerkin Methods,ible and (nearly) incompressible materials, a reasonable question is how these problems can be solved. For most cases in engineering practice, the problems, including their geometry, are too complex for the feasible derivation of an exact analytical solution even though such a solution exists. We ar

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Numerical Integration,ical integration schemes are required to evaluate the integrals that appear in the Galerkin weak forms presented in the preceding chapter for both mesh-based and meshfree methods. First, the classical Gauss quadrature scheme is explained before the more modern stabilized conforming nodal integration

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Energy Norm A Posteriori Error Estimates,estigate the question whether the boundary value problems derived in Chaps. 2 and 3 are solved right by the Galerkin methods presented in Chaps. 4 and 5, i.e. the (mixed) finite element method (based on SCNI), the extended finite element method, and the meshfree element-free Galerkin and reproducing

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Goal-oriented A Posteriori Error Estimates in Linearized Elasticity,ost cases, of greater interest to engineers than their energy norm counterparts. The error estimation procedures presented in the previous chapter for both Galerkin mesh-based and meshfree methods are extended in this chapter to provide an estimation of the generalized error measure. This error meas

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Goal-oriented A Posteriori Error Estimates in Finite Hyperelasticity,elasticity problem within both Newtonian and Eshelbian mechanics are derived for compressible and (nearly) incompressible materials. These error estimation procedures represent the most challenging ones presented in this monograph from both theoretical and numerical points of view. As a consequence,