Related papers: A mortar method for the coupled Stokes-Darcy probl…
This paper discusses and analyses two domain decomposition approaches for electromagnetic problems that allow the combination of domains discretised by either N\'ed\'elec-type polynomial finite elements or spline-based isogeometric…
The multimesh finite element method is a technique for solving partial differential equations on multiple non-matching meshes by enforcing interface conditions using Nitsche's method. Since the non-matching meshes can result in arbitrarily…
In this paper, we propose a numerical method for the solution of time-dependent flow problems in mixed form. Such problems can be efficiently approximated on hierarchical grids, obtained from an unstructured coarse triangulation by using a…
We consider an elliptic partial differential equation in non-divergence form with a random diffusion matrix and random forcing term. To address this, we propose a mixed-type continuous finite element discretization in the physical domain,…
We present a simple and efficient variational finite difference method for simulating time-dependent Stokes flow in the presence of irregular free surfaces and moving solid boundaries. The method uses an embedded boundary approach on…
In two and three dimensional domains, we analyze mixed finite element methods for a velocity-pressure-pseudostress formulation of the Stokes eigenvalue problem. The methods consist in two schemes: the velocity and pressure are approximated…
We study a discrete variant of the Airy equation, formulated as an advance-delay equation, to reveal that discretization induces the higher-order Stokes phenomenon, which is not present in the continuous Airy function and is typically only…
We propose a boundary value correction method for the Brezzi-Douglas-Marini mixed finite element discretization of the Darcy flow with non-homogeneous Neumann boundary condition on 2D curved domains. The discretization is defined on a…
Discrete fracture networks is a key ingredient in the simulation of physical processes which involve fluid flow in the underground, when the surrounding rock matrix is considered impervious. In this paper we present two different models to…
Matrix acidization simulation is a challenging task in the study of flows in porous media, due to the changing porosity in the procedure. The improved DBF framework is one model to do this simulation, and its numerical scheme discretises…
We consider a surface Stokes problem in stream function formulation on a simply connected oriented surface $\Gamma \subset \mathbb{R}^3$ without boundary. This formulation leads to a coupled system of two second order scalar surface partial…
Meshless methods inherently do not require mesh topologies and are practically used for solving continuum equations. However, these methods generally tend to have a higher computational load than conventional mesh-based methods because…
We derive a compatible discretization method that relies heavily on the underlying geometric structure, and obeys the topological sequences and commuting properties that are constructed. As a sample problem we consider the…
We present a finite element method for the Stokes equations involving two immiscible incompressible fluids with different viscosities and with surface tension. The interface separating the two fluids does not need to align with the mesh. We…
In this paper, we propose a parameter-robust preconditioner for the coupled Stokes-Darcy problem equipped with various boundary conditions, enforcing the mass conservation at the interface via a Lagrange multiplier. We rigorously establish…
Stability and error analysis of a hybridized discontinuous Galerkin finite element method for Stokes equations is presented. The method is locally conservative, and for particular choices of spaces the velocity field is point-wise…
This paper addresses the challenge of proving the existence of solutions for nonlinear equations in Banach spaces, focusing on the Navier-Stokes equations and discretizations of thom. Traditional methods, such as monotonicity-based…
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…
We consider implementational aspects of the mixed finite element method for a special class of nonlinear problems. We establish the equivalence of the hybridized formulation of the mixed finite element method to a nonconforming finite…
Solving the linear elasticity and Stokes equations by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions. The one-level domain decomposition preconditioners are based on the…