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Titlebook: Numerical Methods for Nonlinear Partial Differential Equations; Sören Bartels Book 2015 Springer International Publishing Switzerland 2015

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Elastoplasticityimal a priori and a posteriori error estimates for low-order finite element methods are derived. The numerical implementation requires solving a nonlinear, nonsmooth equation at every time step whose realization is based on eliminating the plastic strain. Short codes that realize different types of plastic material behavior are provided.
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The Allen–Cahn Equationthis dependence. Applying those estimates to analyzing approximation schemes for the simplest case of the Allen–Cahn equation in terms of a priori and a posteriori error estimates is carried out. The stability of various implicit and semi-implicit time-stepping schemes is discussed.
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