Abstract. The optimal design problem for maximal torsion stiffness of an infinite bar of given geometry and unknown distribution of two materials of prescribed amounts is one model example in topology optimisation. It ...

A unified and robust mathematical model for compressible and incompressible linear elasticity can be obtained by rephrasing the Herrmann formulation within the Hellinger-Reissner principle. This quasi-optimally converging ...

The nonconforming virtual element method (NCVEM) for the approximation of the weak solution to a general linear second-order non-selfadjoint indefinite elliptic PDE in a polygonal domain Ω is analyzed under reduced elliptic ...

Residual-based a posteriori error estimates are derived wihtin a unified setting for lowest-order conforming, nonconforming, and mixed finite element schemes. The various residuals are identified for all techniques and ...

A class of degenerate convex minimization problems allows for some adaptive finite element method (AFEM) to compute strongly converging stress approximations. The algorithm AFEM consists of successive loops of the form ...

An adaptive mixed finite element method (AMFEM) is designed to guarantee an error reduction, also known as saturation property: After each refinement step, the error for the fine mesh is strictly smaller than the error for ...

This paper establishes a unified framework for the a posteriori error analysis of a large class of nonconforming finite element methods. The theory assures reliability and efficiency of explicit residual error estimates ...

For a well-posed non-selfadjoint indefinite second-order linear elliptic PDE with general coefficients A, b, γ in L∞ and symmetric and uniformly positive definite coefficient matrix A, this paper proves that mixed finite ...

This paper summarises the general strategy for time evolving finite elastoplasticity and outlines encountered computational challenges in form of numerical benchmarks. Each time-step of some natural implicit time-discretisation ...