相关论文: Mesh Quality Metrics for Isogeometric Bernstein-B\…

In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. We consider a new unfitted finite element method…

Mesh adaptivity is a useful tool for efficient solution to partial differential equations in very complex geometries. In the present paper we discuss the use of polygonal mesh refinement in order to tackle two common issues: first,…

The typical goal of surface remeshing consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper…

A mesh improvement methodology is pre- sented which aims to improve the quality of the worst elements in 3D meshes with non-planar surfaces which cannot be improved using traditional methods. A nu- merical optimisation algorithm, which…

Finite element approximations of minimal surface are not always precise. They can even sometimes completely collapse. In this paper, we provide a simple and inexpensive method, in terms of computational cost, to improve finite element…

We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are…

During design optimization, a smooth description of the geometry is important, especially for problems that are sensitive to the way interfaces are resolved, e.g., wave propagation or fluid-structure interaction. A levelset description of…

Higher-order numerical methods are used to find accurate numerical solutions to hyperbolic partial differential equations and equations of transport type. Limiting is required to either converge to the correct type of solution or to adhere…

In this paper we present a new Eulerian finite element method for the discretization of scalar partial differential equations on evolving surfaces. In this method we use the restriction of standard space-time finite element spaces on a…

In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While standard multilevel methods are effective for uniform…

A mesh-based parametrization is a parametrization of a geometric object that is defined solely from a mesh of the object, e.g., without an analytical expression or computer-aided design (CAD) representation of the object. In this work, we…

A higher-order fictitious domain method (FDM) for Reissner-Mindlin shells is proposed which uses a three-dimensional background mesh for the discretization. The midsurface of the shell is immersed into the higher-order background mesh and…

Maximal regularity is a fundamental concept in the theory of partial differential equations. In this paper, we establish a fully discrete version of maximal regularity for a parabolic equation. We derive various stability results in…

In this work we present an extension of the Virtual Element Method with curved edges for the numerical approximation of the second order wave equation in a bidimensional setting. Curved elements are used to describe the domain boundary, as…

We introduce new Hermite-style and Bernstein-style geometric decompositions of the cubic order serendipity finite element spaces $S_3(I^2)$ and $S_3(I^3)$, as defined in the recent work of Arnold and Awanou [Found. Comput. Math. 11 (2011),…

This work extends the concepts of algebraic flux correction and convex limiting to continuous high-order Bernstein finite element discretizations of scalar hyperbolic problems. Using an array of adjustable diffusive fluxes, the standard…

The locally modified finite element method, which is introduced in [Frei, Richter: SINUM 52(2014), p. 2315-2334], is a simple fitted finite element method that is able to resolve weak discontinuities in interface problems. The method is…

We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…

This work focuses on model preparation for electrostatic simulations of CAD designs to realize a rapid virtual prototyping concept. We present a boundary element method (BEM) allowing discontinuous fields between surfaces. The corresponding…

This paper proposes a low order geometrically exact flexible beam formulation based on the utilisation of generic beam shape functions to approximate distributed kinematic properties of the deformed structure. The proposed nonlinear beam…