Related papers: A mixed discontinuous/continuous finite element pa…
In this article, we analyse a stabilised equal-order finite element approximation for the Stokes equations on anisotropic meshes. In particular, we allow arbitrary anisotropies in a sub-domain, for example along the boundary of the domain,…
Currently existing energy-stable parametric finite element methods for surface diffusion flow and other flows are usually limited to first-order accuracy in time. Designing a high-order algorithm for geometric flows that can also be…
We introduce a pressure robust Finite Element Method for the linearized Magnetohydrodynamics equations in three space dimensions, which is provably quasi-robust also in the presence of high fluid and magnetic Reynolds numbers. The proposed…
A finite element (FE) discretization for the steady, incompressible, fully inhomogeneous, generalized Navier-Stokes equations is proposed. By the method of divergence reconstruction operators, the formulation is valid for all shear stress…
This work presents a general finite element formulation based on a six--field variational principle that incorporates the consistent couple stress theory. A simple, efficient and local iteration free solving procedure that covers both…
One of the key choices for numerical models of geophysical fluids is how parametrisations of physical processes interact with the numerical methods that handle the resolved flow, known in the atmospheric community as the dynamical core. As…
This work is a contribution to the understanding of the question of stability of Perfectly Matched Layers (PMLs) in corners, at continuous and discrete levels. First, stability results are presented for the Cartesian PMLs associated to a…
This work develops a convergence theory for H(div)-conforming finite element methods applied to the steady Oseen problem, focusing on cases where the exact finite element complex holds while the commuting diagram property may fail. The…
We introduce a hybrid method to couple continuous Galerkin finite element methods and high-order finite difference methods in a nonconforming multiblock fashion. The aim is to optimize computational efficiency when complex geometries are…
In this paper, a symmetrized two-scale finite element method is proposed for a class of partial differential equations with symmetric solutions. With this method, the finite element approximation on a fine tensor product grid is reduced to…
In this contribution, a finite element scheme to impose mixed boundary conditions without introducing Lagrange multipliers is presented for hyperbolic systems described as port-Hamiltonian systems. The strategy relies on finite element…
Methods for discretizing port-Hamiltonian systems are of interest both for simulation and control purposes. Despite the large literature on mixed finite elements, no rigorous analysis of the connections between mixed elements and…
We provide an approach to implementing the shallow atmosphere approximation in three dimensional finite element discretisations for dynamical cores. The approach makes use of the fact that the shallow atmosphere approximation metric can be…
Starting with a static, spherically symmetric spacetime incorporating critical (unstable) closed null geodesics, a family of models for equilibrium states of non-isolated compact objects is obtained by solving the Einstein equations for an…
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…
We present a mechanism to explicitly couple the finite-difference discretizations of 2D acoustic and isotropic elastic wave systems that are separated by straight interfaces. Such coupled simulations allow the application of the elastic…
In the framework of a mixed finite element method, a structure-preserving formulation for incompressible magnetohydrodynamic (MHD) equations with general boundary conditions is proposed. A leapfrog-type temporal scheme fully decouples the…
An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the…
A well-designed numerical method for the shallow water equations (SWE) should ensure well-balancedness, nonnegativity of water heights, and entropy stability. For a continuous finite element discretization of a nonlinear hyperbolic system…
A first-order system least squares formulation for the sea-ice dynamics is presented. In addition to the displacement field, the stress tensor is used as a variable. As finite element spaces, standard conforming piecewise polynomials for…