相关论文: Parallel implementation of a compatible high-order…

We design and investigate efficient multigrid solvers for multiphase Stokes problems discretised via mixed-degree local discontinuous Galerkin methods. Using the template of a standard multigrid V-cycle, we develop a smoother analogous to…

Surface Stokes and Navier-Stokes equations are used to model fluid flow on surfaces. They have attracted significant recent attention in the numerical analysis literature because approximation of their solutions poses significant challenges…

Variable viscosity arises in many flow scenarios, often imposing numerical challenges. Yet, discretisation methods designed specifically for non-constant viscosity are few, and their analysis is even scarcer. In finite element methods for…

We present a monolithic geometric multigrid preconditioner for solving fluid-solid interaction problems in Stokes limit. The problems are discretized by a spatially adaptive high-order meshless method, the generalized moving least squares…

We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex---possibly nonsmooth---geometries in two dimensions. The key ingredient is a set of panel quadrature rules capable of…

In this paper, we consider the Stokes problem with Dirichlet boundary conditions and the constant kinematic viscosity $\nu$ in an axis-aligned domain $\Omega$. We decouple the velocity $\bm u$ and pressure $p$ by deriving a novel biharmonic…

The hybrid-high order (HHO) scheme has many successful applications including linear elasticity as the first step towards computational solid mechanics. The striking advantage is the simplicity among other higher-order nonconforming schemes…

The paper describes a sparse direct solver for the linear systems that arise from the discretization of an elliptic PDE on a two dimensional domain. The scheme decomposes the domain into thin subdomains, or ``slabs'' and uses a two-level…

In this paper, we design a novel algorithm based on Least-Squares Monte Carlo (LSMC) in order to approximate the solution of discrete time Backward Stochastic Differential Equations (BSDEs). Our algorithm allows massive parallelization of…

In this paper we present an arbitrary-order fully discrete Stokes complex on general polyhedral meshes. We enriche the fully discrete de Rham complex with the addition of a full gradient operator defined on vector fields and fitting into…

In this paper, we propose a ${ P_{1}^{c}}\oplus {RT0}-P0$ discretization of the Stokes equations on general simplicial meshes in two/three dimensions (2D/3D), which yields an exactly divergence-free and pressure-independent velocity…

This paper develops divergence-free mixed finite element methods for the Stokes equation. Using H(div)-conforming velocities and discontinuous pressures ensures the inf-sup condition for the velocity--pressure pair and yields pointwise…

This work presents a high-accuracy, mesh-free, generalized Stokes theorem-based numerical quadrature scheme for integrating functions over trimmed parametric surfaces and volumes. The algorithm relies on two fundamental steps: (1) We…

We consider a stabilization method for divergence-conforming B-spline discretizations of the incompressible Navier--Stokes problem wherein jumps in high-order normal derivatives of the velocity field are penalized across interior mesh…

A discontinuous Galerkin method by patch reconstruction is proposed for Stokes flows. A locally divergence-free reconstruction space is employed as the approximation space, and the interior penalty method is adopted which imposes the normal…

Incompressible flow solvers based on strong-form meshfree methods represent arbitrary geometries without the need for a global mesh system. However, their local evaluations make it difficult to satisfy incompressibility at the discrete…

In the present paper we develop a new family of Virtual Elements for the Stokes problem on polygonal meshes. By a proper choice of the Virtual space of velocities and the associated degrees of freedom, we can guarantee that the final…

In this paper we present an all-at-once multigrid method for a distributed Stokes control problem (velocity tracking problem). For solving such a problem, we use the fact that the solution is characterized by the optimality system…

We propose a new least squares finite element method to solve the Stokes problem with two sequential steps. The approximation spaces are constructed by patch reconstruction with one unknown per element. For the first step, we reconstruct an…

This paper proposes a parallel numerical algorithm to simulate the flow and the transport in a discrete fracture network taking into account the mass exchanges with the surrounding matrix. The discretization of the Darcy fluxes is based on…