Related papers: Divergence-free unfitted finite element discretisa…
In this work we propose a nonlinear stabilization technique for convection-diffusion-reaction and pure transport problems discretized with space-time isogeometric analysis. The stabilization is based on a graph-theoretic artificial…
We implement a stabilized finite element method for steady Darcy-Brinkman-Forchheimer model within the continuous Galerkin framework. The nonlinear fluid model is first linearized using a standard \textit{Newton's method. The sequence of…
In this paper, we develop a modified nonlinear dynamic diffusion (DD) finite element method for convection-diffusion-reaction equations. This method is free of stabilization parameters and is capable of precluding spurious oscillations. We…
We present a discretization for Darcy's problem using the recently developed Mimetic Spectral Element Method. The gist lies in the exact discrete representation of integral relations. In this paper, an anisotropic flow through a porous…
The dynamics of thermally fluctuating conserved order parameters are described by stochastic conservation laws. Thermal equilibrium in such systems requires the dissipative and stochastic components of the flux to be related by detailed…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…
Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier…
This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inter-element solution discontinuities, such as discontinuous…
We present a one-dimensional high-order moving-mesh finite element method for moving boundary problems where the boundary velocity depends implicitly on the solution in the interior of the domain. The method employs a conservative arbitrary…
A finite element analysis of a Dirichlet boundary control problem governed by the linear parabolic equation is presented in this article. The Dirichlet control is considered in a closed and convex subset of the energy space $H^1(\Omega…
We study the existence of solutions for Darcy's problem coupled with the heat equation under singular forcing; the right-hand side of the heat equation corresponds to a Dirac measure. The studied model allows thermal diffusion and viscosity…
In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…
We present a geometric variational discretization of nonlinear elasticity in 2D and 3D in the Lagrangian description. A main step in our construction is the definition of discrete deformation gradients and discrete Cauchy-Green deformation…
The convergence and optimality of adaptive mixed finite element methods for the Poisson equation are established in this paper. The main difficulty for mixed finite element methods is the lack of minimization principle and thus the failure…
We describe an energy-enstrophy conserving discretisation for the rotating shallow water equations with slip boundary conditions. This relaxes the assumption of boundary-free domains (periodic solutions or the surface of a sphere, for…
We derive a numerical method for Darcy flow, hence also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is…
In this paper, we propose a novel high order unfitted finite element method on Cartesian meshes for solving the acoustic wave equation with discontinuous coefficients having complex interface geometry. The unfitted finite element method…
In this paper we discretize the incompressible Navier-Stokes equations in the framework of finite element exterior calculus. We make use of the Lamb identity to rewrite the equations into a vorticity-velocity-pressure form which fits into…
We consider a numerical approximation of a linear quadratic control problem constrained by the stochastic heat equation with non-homogeneous Neumann boundary conditions. This involves a combination of distributed and boundary control, as…