There have been many efforts, dating back four decades, to develop stablemixed finite elements for the stress-displacement formulation of the plane elasticity system. This requires the development of a compatible pair of finite element spaces, one to discretize the space of symmetric tensors in which the stress field is sought, and one to discretize the space of vector fields in which the displ...

This paper describes the prototype of a facial expression editor. In contrast to existing systems the presented editor takes advantage of both medical data for the simulation and the consideration of facial anatomy during the definition of muscle groups. The C1-continuous geometry and the high degree of abstraction for the expression editing sets this system apart from others. Using finite elem...

This paper discusses FEM-based simulations of soft bodies in terms of speed and robustness. To be physically plausible, three fundamental laws must be respected: rotational invariance, Newton’s law and Euler’s law. We show that precomputed strain-displacement matrices generate nonphysical torques which can lead to visual artifacts. We then derive the fastest FEM-based method meeting our criteri...

In this paper, we present new Gaussian integration schemes for the efficient and accurate evaluation of weak form integrals that arise in enriched finite element methods. For discontinuous functions we present an algorithm for the construction of Gauss-like quadrature rules over arbitrarily-shaped elements without partitioning. In case of singular integrands, we introduce a new polar transforma...

In this paper we analyse a sub-domain residual error estimator for finite element approximations of elliptic problems. It is obtained by solving local problems on patches of elements in weighted spaces and provides for an upper bound on the energy norm of the error when the local problems are solved in sufficiently enriched discrete spaces. A guaranteed lower bound on the error is also derived ...

‎Let $G$ be a finite group‎. ‎An element $gin G$ is called non-vanishing‎, ‎if for‎ ‎every irreducible complex character $chi$ of $G$‎, ‎$chi(g)neq 0$‎. ‎The bi-Cayley graph ${rm BCay}(G,T)$ of $G$ with respect to a subset $Tsubseteq G$‎, ‎is an undirected graph with‎ ‎vertex set $Gtimes{1,2}$ and edge set ${{(x,1),(tx,2)}mid xin G‎, ‎ tin T}$‎. ‎Let ${rm nv}(G)$ be the set‎ ‎of all non-vanishi...

In this paper, we introduce a new family of mixed finite element spaces of higher order (k ≥ 1) on general quadrilateral grids. A typical element has two fewer degrees of freedom than the well-known RaviartThomas finite element RT[k], yet enjoys an optimal-order approximation for the velocity in L 2-norm. The order of approximation in the divergence norm is one less than the velocity, as is com...

I review the main ideas behind the construction of edge elements of variable order 16, 39, 18], and discuss the possibility of extending the construction to Nedelec's elements of the rst kind 31]. A motivation leading to the deenition of hp-interpolation operators is highlighted, and their impact on the hp-discretizations of Maxwell's equations discussed.

The mixed variational formulation of many elliptic boundary value problems involves vector valued function spaces, like, in three dimensions, H(curl; Ω) and H(Div;Ω). Thus finite element subspaces of these function spaces are indispensable for effective finite element discretization schemes. Given a simplicial triangulation of the computational domain Ω, among others, Raviart, Thomas and Nédéle...