Related papers: $hp$-Multigrid preconditioner for a divergence-con…
We present the lowest-order hybridizable discontinuous Galerkin schemes with numerical integration (quadrature), denoted as HDG-P0, for the reaction-diffusion equation and the generalized Stokes equations on conforming simplicial meshes in…
We present a monolithic hp space-time multigrid method (hp-STMG) for tensor-product space-time finite element discretizations of the incompressible Navier-Stokes equations. We employ mapped inf-sup stable pairs $\mathbb Q_{r+1}/\mathbb…
We address the solution of the distributed control problem for the steady, incompressible Navier--Stokes equations. We propose an inexact Newton linearization of the optimality conditions. Upon discretization by a finite element scheme, we…
We present a monolithic geometric multigrid preconditioner for solving fluid-solid interaction problems in Stokes limit. The problems are discretized by a spatially adaptive high-order meshless method, the generalized moving least squares…
We investigate a novel monolithic algebraic multigrid (AMG) preconditioner for the Taylor-Hood ($\pmb{\mathbb{P}}_2/\mathbb{P}_1$) and Scott-Vogelius ($\pmb{\mathbb{P}}_2/\mathbb{P}_1^{disc}$) discretizations of the Stokes equations. The…
In this work we exploit agglomeration based $h$-multigrid preconditioners to speed-up the iterative solution of discontinuous Galerkin discretizations of the Stokes and Navier-Stokes equations. As a distinctive feature $h$-coarsened mesh…
We present a monolithic $hp$ space-time multigrid method for tensor-product space-time finite element discretizations of the Stokes equations. Geometric and polynomial coarsening of the space-time mesh is performed, and the entire algorithm…
In this paper, we present a geometric multigrid methodology for the solution of matrix systems associated with isogeometric compatible discretizations of the generalized Stokes and Oseen problems. The methodology provably yields a pointwise…
Numerical solution of discrete PDEs corresponding to saddle point problems is highly relevant to physical systems such as Stokes flow. However, scaling up numerical solvers for such systems is often met with challenges in efficiency and…
A fast multigrid solver is presented for high-order accurate Stokes problems discretised by local discontinuous Galerkin (LDG) methods. The multigrid algorithm consists of a simple V-cycle, using an element-wise block Gauss-Seidel smoother.…
We propose a multigrid method to solve the linear system of equations arising from a hybrid discontinuous Galerkin (in particular, a single face hybridizable, a hybrid Raviart--Thomas, or a hybrid Brezzi--Douglas--Marini) discretization of…
The numerical analysis of higher-order mixed finite-element discretizations for saddle-point problems, such as the Stokes equations, has been well-studied in recent years. While the theory and practice of such discretizations is now…
In this paper we present a numerical approach to solve the Navier-Stokes equations on moving domains with second-order accuracy. The space discretization is based on the ghost-point method, which falls under the category of unfitted…
In this paper we propose a novel arbitrary high order accurate semi-implicit space-time DG method for the solution of the three-dimensional incompressible Navier-Stokes equations on staggered unstructured curved tetrahedral meshes. As…
We present an optimal preconditioner for the exactly divergence-free discontinuous Galerkin (DG) discretization of Cockburn, Kanschat, and Sch\"otzau [J. Sci. Comput., 31 (2007), pp. 61--73] and Wang and Ye [SIAM J. Numer. Anal., 45 (2007),…
A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a…
We present a superconvergent hybridizable discontinuous Galerkin (HDG) method for the steady-state incompressible Navier-Stokes equations on general polyhedral meshes. For arbitrary conforming polyhedral mesh, we use polynomials of degree…
A well-known strategy for building effective preconditioners for higher-order discretizations of some PDEs, such as Poisson's equation, is to leverage effective preconditioners for their low-order analogs. In this work, we show that…
Algebraic multigrid (AMG) preconditioners are considered for discretized systems of partial differential equations (PDEs) where unknowns associated with different physical quantities are not necessarily co-located at mesh points.…
In a recent work [10], we have introduced a pressure-robust Hybrid High-Order method for the numerical solution of the incompressible Navier-Stokes equations on matching simplicial meshes. Pressure-robust methods are characterized by error…