Related papers: A finite element approach for vector- and tensor-v…
A unified construction of $H(\textrm{div})$-conforming finite element tensors, including vector element, symmetric matrix element, traceless matrix element, and, in general, tensors with linear constraints, is developed in this work. It is…
We develop a finite element method for a large deformation membrane elasticity problem on meshed surfaces using a tangential differential calculus approach that avoids the use of classical differential geometric methods. The method is also…
We develop finite element spaces of symmetric tensor products of two-forms with polynomial coefficients. In three dimensions, these give higher order finite element spaces of matrix fields with normal-normal continuity, which have…
In this paper we consider a class of unfitted finite element methods for discretization of partial differential equations on surfaces. In this class of methods known as the Trace Finite Element Method (TraceFEM), restrictions or traces of…
We introduce and extend the outer product and contractive product of tensors and matrices, and present some identities in terms of these products. We offer tensor expressions of derivatives of tensors, focus on the tensor forms of…
This paper presents an innovative continuous linear finite element approach to effectively solve biharmonic problems on surfaces. The key idea behind this method lies in the strategic utilization of a surface gradient recovery operator to…
We develop a finite element method for elliptic partial differential equations on so called composite surfaces that are built up out of a finite number of surfaces with boundaries that fit together nicely in the sense that the intersection…
We present a continuous finite element method for some examples of fully nonlinear elliptic equation. A key tool is the discretisation proposed in Lakkis & Pryer (2011, SISC) allowing us to work directly on the strong form of a linear PDE.…
In this paper, we extend the classical quadrilateral based hierarchical Poincar\'e-Steklov (HPS) framework to triangulated geometries. Traditionally, the HPS method takes as input an unstructured, high-order quadrilateral mesh and relies on…
We develop a geometrically intrinsic formulation of the arbitrary-order Virtual Element Method (VEM) on polygonal cells for the numerical solution of elliptic surface partial differential equations (PDEs). The PDE is first written in…
The paper introduces a finite element method for the incompressible Navier--Stokes equations posed on a closed surface $\Gamma\subset\R^3$. The method needs a shape regular tetrahedra mesh in $\mathbb{R}^3$ to discretize equations on the…
We consider finite element approximations of the Maxwell eigenvalue problem in two dimensions. We prove, in certain settings, convergence of the discrete eigenvalues using Lagrange finite elements. In particular, we prove convergence in…
This paper is concerned with solving some structured multi-linear systems, which are called tensor absolute value equations. This kind of absolute value equations is closely related to tensor complementarity problems and is a generalization…
We consider a numerical approach for the incompressible surface Navier-Stokes equation on surfaces with arbitrary genus $g(\mathcal{S})$. The approach is based on a reformulation of the equation in Cartesian coordinates of the embedding…
In this paper we study semi-discrete and fully discrete evolving surface finite element schemes for the Cahn-Hilliard equation with a logarithmic potential. Specifically we consider linear finite elements discretising space and backward…
In this work, we propose a mixed finite element method for solving elliptic multiscale problems based on a localized orthogonal decomposition (LOD) of Raviart-Thomas finite element spaces. It requires to solve local problems in small…
In this paper a class of higher order finite element methods for the discretization of surface Stokes equations is studied. These methods are based on an unfitted finite element approach in which standard Taylor-Hood spaces on an underlying…
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…
This paper is a generalization of the previous work (Yang et.al, J. Comput. Phys. 330 (2017), 863-883) to the 3-D irregular convex domains. The analytical calculation formula of fractional derivatives of finite element basis functions are…
We study the geodesic X-ray transform on Cartan-Hadamard manifolds, and prove solenoidal injectivity of this transform acting on functions and tensor fields of any order. The functions are assumed to be exponentially decaying if the…