Related papers: Highly sparse surface couplings for subdomain-wise…
This article presents a higher-order spectral element method for the two-dimensional Stokes interface problem involving a piecewise constant viscosity coefficient. The proposed numerical formulation is based on least-squares formulation.…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
Provable stable arbitrary order symmetric interior penalty discontinuous Galerkin (SIP) discretisations of variable viscosity, incompressible Stokes flow utilising $Q^2_k$--$Q_{k-1}$ elements and hierarchical Legendre basis polynomials are…
In this work, we analyze an unfitted discontinuous Galerkin discretization for the numerical solution of the Stokes system based on equal higher-order discontinuous velocities and pressures. This approach combines the best from both worlds,…
Pointwise divergence free velocity field approximations of the Stokes system are gaining popularity due to their necessity in precise modelling of physical flow phenomena. Several methods have been designed to satisfy this requirement;…
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…
A non-overlapping domain decomposition algorithm is proposed to solve the linear system arising from mixed finite element approximation of incompressible Stokes equations. A continuous finite element space for the pressure is used. In the…
This paper presents a gradient-based reconstruction approach for simulations of compressible single and multi-species Navier-Stokes equations. The novel feature of the proposed algorithm is the efficient reconstruction via derivative…
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…
We study the iterative solution of linear systems of equations arising from stochastic Galerkin finite element discretizations of saddle point problems. We focus on the Stokes model with random data parametrized by uniformly distributed…
We present a finite-difference scheme which solves the Stokes problem in the presence of curvilinear non-conforming interfaces and provides second-order accuracy on physical field (velocity, vorticity) and especially on pressure. The gist…
The computational homogenization of hyperelastic solids in the geometrically nonlinear context has yet to be treated with sufficient efficiency in order to allow for real-world applications in true multiscale settings. This problem is…
In this article, we discuss gradient robust discretizations for the simulation of non-linear incompressible Navier-Stokes problem and the optimal control of such flow. We consider several formulations of the flow problem that are equivalent…
Unfitted boundary methods are widely used to numerically solve partial differential equations (PDEs) on irregular domains, avoiding the computational burden of generating boundary-conforming grids. In the finite-difference framework,…
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…
We propose a new discretization method for the Stokes equations. The method is an improved version of the method recently presented in [C. Lehrenfeld, J. Sch\"oberl, Comp. Meth. Appl. Mech. Eng., 361 (2016)] which is based on an…
In this work, we develop and analyse a novel Hybrid High-Order discretisation of the Brinkman problem. The method hinges on hybrid discrete velocity unknowns at faces and elements and on discontinuous pressures. Based on the discrete…
This paper describes the recently developed mixed mimetic spectral element method for the Stokes problem in the vorticity-velocity-pressure formulation. This compatible discretization method relies on the construction of a conforming…
In this study, a stabilized finite element analysis of unified Stokes-Darcy-Brinkman system fully coupled with variable coefficient Advection-Diffusion-Reaction equation(VADR) has been carried out. The viscosity of the fluid, involved in…
We present a Ritz-Galerkin discretization on sparse grids using pre-wavelets, which allows to solve elliptic differential equations with variable coefficients for dimension $d=2,3$ and higher dimensions $d>3$. The method applies multilinear…