Related papers: Efficient Assembly of H(div) and H(curl) Conformin…
Finite elements of higher continuity, say conforming in $H^2$ instead of $H^1$, require a mapping from reference cells to mesh cells which is continuously differentiable across cell interfaces. In this article, we propose an algorithm to…
Robust mixed finite element methods are developed for a quad-curl singular perturbation problem. Lower order H(grad curl)-nonconforming but H(curl)-conforming finite elements are constructed, which are extended to nonconforming finite…
In [24], we proposed H(curl^2)-conforming elements on both a triangle and a rectangle. This family of elements provides a brand new method to solve the quad-curl problem in 2 dimensions. In this paper, we turn our focus to 3 dimensions and…
In this paper, we introduce a novel a posteriori error estimator for the conforming finite element approximation to the H(curl) problem with inhomogeneous media and with the right-hand side only in L^2. The estimator is of the recovery…
We generalize the two dimensional mixed finite elements of Arbogast and Correa [T. Arbogast and M. R. Correa, SIAM J. Numer. Anal., 54 (2016), pp. 3332--3356] defined on quadrilaterals to three dimensional cuboidal hexahedra. The…
This work introduces a novel, fully robust and highly-scalable, $h$-adaptive aggregated unfitted finite element method for large-scale interface elliptic problems. The new method is based on a recent distributed-memory implementation of the…
A variational framework, initially developed for high-order mesh optimisation, is being extended for r-adaptation. The method is based on the minimisation of a functional of the mesh deformation. To achieve adaptation, elements of the…
Spectral element methods (SEM), which are extensions of finite element methods (FEM), are important emerging techniques for solving partial differential equations in physics and engineering. SEM can potentially deliver better accuracy due…
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 discuss realization, properties and performance of the adaptive finite element approach to the design of nano-photonic components. Central issues are the construction of vectorial finite elements and the embedding of bounded components…
We investigate the compilation of general multilinear variational forms over affines simplices and prove a representation theorem for the representation of the element tensor (element stiffness matrix) as the contraction of a constant…
This is a study of certain finite element methods designed for convection-dominated, time-dependent partial differential equations. Specifically, we analyze high order space-time tensor product finite element discretizations, used in a…
In this paper we present a new H(div)-conforming unfitted finite element method for the mixed Poisson problem which is robust in the cut configuration and preserves conservation properties of body-fitted finite element methods. The key is…
We propose a finite element discretisation approach for the incompressible Euler equations which mimics their geometric structure and their variational derivation. In particular, we derive a finite element method that arises from a…
The Hilbert spaces $H(\mathrm{curl})$ and $H(\mathrm{div})$ are needed for variational problems formulated in the context of the de Rham complex in order to guarantee well-posedness. Consequently, the construction of conforming subspaces is…
A new $H(\textrm{divdiv})$-conforming finite element is presented, which avoids the need for super-smoothness by redistributing the degrees of freedom to edges and faces. This leads to a hybridizable mixed method with superconvergence for…
In this work, an adaptive edge element method is developed for an H(curl)-elliptic constrained optimal control problem. We use the lowest-order Nedelec's edge elements of first family and the piecewise (element-wise) constant functions to…
One approach for the simulation of metamaterials is to extend an associated continuum theory concerning its kinematic equations, and the relaxed micromorphic continuum represents such a model. It incorporates the Curl of the nonsymmetric…
Thanks to modern manufacturing technologies, heterogeneous materials with complex inner structures (e.g., foams) can be easily produced. However, their utilization is not straightforward, as the classical constitutive laws are not…
We present a new set of basis functions for H(curl)-conforming, H(div)-conforming, and L2 -conforming finite elements of arbitrary order on a tetrahedron. The basis functions are expressed in terms of Bernstein polynomials and augment the…