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

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Harmonic MapsThe solutions are vector fields that describe the orientation of the molecules or the magnetization field. A simple model problem defines harmonic maps in the sphere as minimizers of the Dirichlet energy subject to a pointwise unit-length constraint. Lowest-order conforming finite element methods pr

chronicle

Bending Problems fourth-order problems. In the case of small displacements, a linear partial differential equation provides accurate approximations, but finite element methods have to be carefully developed to avoid locking phenomena. In the case of large deformations, a pointwise isometry constraint has to be inco

CLEFT

Nonconvexity and Microstructurel descriptions of crystalline phase transitions that enable the shape-memory effect of smart materials. The ill-posed minimization problems capture important effects and relaxation theories define well-posed modifications of the functionals. The problems related to direct numerical treatment of the

ANTH

Free Discontinuitiesdients of functions of bounded variation are certain measures and the functions may jump across lower-dimensional subsets. The properties of this function space enable the mathematical modeling of fracture and crack formation of materials within the framework of the calculus of variations. Qualitati

BUCK

Elastoplasticitymathematical descriptions lead to nonsmooth evolution problems that can be approximated by sequences of convex minimization problems. Related quasioptimal a priori and a posteriori error estimates for low-order finite element methods are derived. The numerical implementation requires solving a nonli

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