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A new higher-order accurate method is proposed that combines the advantages of the classical p-version of the FEM on body-fitted meshes with embedded domain methods. A background mesh composed by higher-order Lagrange elements is used. Boundaries and interfaces are described implicitly by the level set method and are within elements. In the elements cut by the boundaries or interfaces, an automatic decomposition into higher-order accurate sub-elements is realized. Therefore, the zero level sets are detected and meshed in a first step, which is called reconstruction. Then, based on the topological situation in the cut element, higher-order sub-elements are mapped to the two sides of the boundary or interface. The quality of the reconstruction and the mapping largely determines the properties of the resulting, automatically generated conforming mesh. It is found that optimal convergence rates are possible although the resulting sub-elements are not always well-shaped. [ABSTRACT FROM AUTHOR]

A method is presented which enables the global enrichment of the approximation space without introducing additional unknowns. Only one shape function per node is used. The shape functions are constructed by means of the moving least-squares method with an intrinsic basis vector and weight functions based on finite element shape functions. The enrichment is achieved through the intrinsic basis. By using polynomials in the intrinsic basis, optimal rates of convergence can be achieved even on distorted elements. Special enrichment functions can be chosen to enhance accuracy for solutions that are not polynomial in character. Results are presented which show optimal convergence on randomly distorted elements and improved accuracy for the oscillatory solution of the Helmholtz equation. [ABSTRACT FROM AUTHOR]

Numerical simulations of structures using higher-order finite elements is still a challenging task, in particular for domains with curved boundaries. A new higher-order accurate approach is proposed, combining the advantages of the classical p-FEM with embedded domain methods. Boundaries and/or interfaces are described implicitly using the level set method. In the elements cut by the zero level set, an automatic decomposition into interface aligned, i. e. conforming sub-elements is realized. Transfinite mappings are utilized to construct higher-order sub-elements by mappings of reference elements to the two sides of the boundary or interface. It is shown that although the resulting sub-elements are not always well-shaped, optimal convergence rates are possible. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In this work, an approach is presented to improve global accuracy properties for physically non-linear problems in the frame of elastoplasticity. The work is motivated by the fact that convergence characteristics of a finite element solution are dominated by the regularity of the exact solution. For a material undergoing inelastic deformations, however, very few analytical solutions for the field variables are known, especially for the displacement field. Considering a simple, one-dimensional example, it is shown that the convergence rates are far from optimal. The reason is explained by establishing ties to a familiar, but more demonstrative problem. In the next section two remedies for the problem, based on the Extended Finite Element Method (XFEM) are presented and discussed, in the last section a 2D-problem is considered. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The isogeometric Nyström method is presented in this paper. The important features of the method are: it allows the analysis of domains described by many different geometry descriptions in computer aided geometric design and it requires only pointwise function evaluations similar to isogeometric collocation methods. The analysis of the computational domain is carried out by means of boundary integral equations, therefore a boundary representation only is required. The method is thoroughly integrated into the isogeometric framework. For example, the regularization of the singular integrals arising is performed with local correction and also the interpolation of the pointwise results is carried out by means of Bézier elements. The isogeometric Nyström method is applied to practical problems solved by the Laplace and the Lamé-Navier equation. Numerical tests show a higher order convergence in two and three dimensions. It is concluded that the approach presented provides a simple and flexible alternative to the methods currently used for solving boundary integral equations, although it does have some limitations. [ABSTRACT FROM AUTHOR]