相关论文: Finite elements for symmetric tensors in three dim…
The numerical solution of a nonlinear and space-fractional anti-diffusive equation used to model dune morphodynamics is considered. Spatial discretization is effected using a finite element method whereas the Crank-Nicolson scheme is used…
We consider time-harmonic linear elasticity equations in domains containing two-dimensional semi-infinite strips. Since for such problems there exist modes with different signs of group and phase velocity, standard perfectly matched layer…
Multiple scale homogenization problems are reduced to single scale problems in higher dimension. It is shown that sparse tensor product Finite Element Methods (FEM) allow the numerical solution in complexity independent of the dimension and…
The fourth-order PDE that models the density variation of smectic A liquid crystals presents unique challenges in its (numerical) analysis beyond more common fourth-order operators, such as the classical biharmonic. While the operator is…
We discuss the construction of finite element spaces of differential forms which satisfy the crucial assumptions of the finite element exterior calculus, namely that they can be assembled into subcomplexes of the de Rham complex which admit…
The scaled boundary finite element method (SBFEM) has recently been employed as an efficient means to model three-dimensional structures, in particular when the geometry is provided as a voxel-based image. To this end, an octree…
Finite element methods usually construct basis functions and quadrature rules for multidimensional domains via tensor products of one-dimensional counterparts. While straightforward, this approach results in integration spaces larger than…
We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element discretization of reduced optimality systems defining the approximate solution of hyperbolic…
This article surveys research on the application of compatible finite element methods to large scale atmosphere and ocean simulation. Compatible finite element methods extend Arakawa's C-grid finite difference scheme to the finite element…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
We present a class of discretisation spaces and H(div)-conformal elements that can be built on any polytope. Bridging the flexibility of the Virtual Element spaces towards the element's shape with the divergence properties of the…
We propose a novel mixed finite-element formulation for geometrically exact (Simo--Reissner) beams that introduces the moment vector as additional independent field. The specific mixed form allows for an element-local, discontinuous…
In this paper, a finite element space is presented on quadrilateral grids which can provide consistent discretization for the biharmonic equations. The space consists of piecewise quadratic polynomials and is of minimal degree for the…
In many applications, thin shell-like structures are integrated within or attached to volumetric bodies. This includes reinforcements placed in soft matrix material in lightweight structure design, or hollow structures that are partially or…
We present a stable finite element method for incompressible nonlinear elasticity based on a four-field mixed formulation involving the displacement, displacement gradient, first Piola--Kirchhoff stress and pressure. Unlike existing…
In [Bonito et al., J. Comput. Phys. (2022)], a local discontinuous Galerkin method was proposed for approximating the large bending of prestrained plates, and in [Bonito et al., IMA J. Numer. Anal. (2023)] the numerical properties of this…
It is well-known that it is comparatively difficult to design nonconforming finite elements on quadrilateral meshes by using Gauss-Legendre points on each edge of triangulations. One reason lies in that these degrees of freedom associated…
We consider the lowest--degree nonconforming finite element methods for the approximation of elliptic problems in high dimensions. The $P_1$--nonconforming polyhedral finite element is introduced for any high dimension. Our finite element…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete system of vectors, called a finite tight frame, may offer…