Related papers: Robust Solvers for Maxwell's Equations with Dissip…
We derive novel, fast, and parameter-robust preconditioned iterative methods for steady and time-dependent Navier--Stokes control problems. Our approach may be applied to time-dependent problems which are discretized using backward Euler or…
In this paper, we revisit an auxiliary space preconditioning method proposed by Xu [Computing 56, 1996], in which low-order finite element spaces are employed as auxiliary spaces for solving linear algebraic systems arising from high-order…
We develop a novel iterative solution method for the incompressible Navier-Stokes equations with boundary conditions coupled with reduced models. The iterative algorithm is designed based on the variational multiscale formulation and the…
High-order implicit shock tracking (fitting) is a class of high-order numerical methods that use numerical optimization to simultaneously compute a high-order approximation to a conservation law solution and align elements of the…
We present two strategies for designing passivity preserving higher order discretization methods for Maxwell's equations in nonlinear Kerr-type media. Both approaches are based on variational approximation schemes in space and time. This…
We develop a robust solver for a mixed finite element convex splitting scheme for the Cahn-Hilliard equation. The key ingredient of the solver is a preconditioned minimal residual algorithm (with a multigrid preconditioner) whose…
The numerical solution of a nonlinear and space-fractional anti-diffusive equation used to model dune morphodynamics is considered. Spatial discretization is effected using a finite element method whereas the Crank-Nicolson scheme is used…
Motivated by a wide range of real-world problems whose solutions exhibit boundary and interior layers, the numerical analysis of discretizations of singularly perturbed differential equations is an established sub-discipline within the…
In this article we develop a high order accurate method to solve the incompressible boundary layer equations in a provably stable manner.~We first derive continuous energy estimates,~and then proceed to the discrete setting.~We formulate…
Numerical discretization of the large-scale Maxwell's equations leads to an ill-conditioned linear system that is challenging to solve. The key requirement for successive solutions of this linear system is to choose an efficient solver. In…
The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially…
In this paper, we propose a new finite element solution approach to the multi-compartmental Darcy equations describing flow and interactions in a porous medium with multiple fluid compartments. We introduce a new numerical formulation and a…
A new conservative finite element solver for the three-dimensional steady magnetohydrodynamic (MHD) kinematics equations is presented.The solver utilizes magnetic vector potential and current density as solution variables, which are…
This article considers the iterative solution of a finite element discretisation of the magma dynamics equations. In simplified form, the magma dynamics equations share some features of the Stokes equations. We therefore formulate, analyse…
Our research focuses on the development of domain decomposition preconditioners tailored for second-order elliptic partial differential equations. Our approach addresses two major challenges simultaneously: i) effectively handling…
We investigate Maxwell-scalar models on radially symmetric spacetimes in which the gauge and scalar fields are coupled via the electric permittivity. We find the conditions that allow for the presence of minimum energy configurations. In…
This work introduces nodal auxiliary space preconditioners for discretizations of mixed-dimensional partial differential equations. We first consider the continuous setting and generalize the regular decomposition to this setting. With the…
We present and analyze two stabilized finite element methods for solving numerically the Poisson--Nernst--Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for…
The solution of matrices with $2\times 2$ block structure arises in numerous areas of computational mathematics, such as PDE discretizations based on mixed-finite element methods, constrained optimization problems, or the implicit or steady…
The paper is devoted to the spectral analysis of effective preconditioners for linear systems obtained via a Finite Element approximation to diffusion-dominated convection-diffusion equations. We consider a model setting in which the…