Related papers: Multigrid Methods for Saddle Point Problems: Darcy…
Predicting the flow of non-Newtonian fluids in porous structure is still a challenging issue due to the interplay betwen the microscopic disorder and the non-linear rheology. In this letter, we study the case of an yield stress fluid in a…
We consider systems of nonlinear magnetostatics and quasistatics that typically arise in the modeling and simulation of electric machines. The nonlinear problems, eventually obtained after time discretization, are usually solved by…
We develop higher order multipoint flux mixed finite element (MFMFE) methods for solving elliptic problems on quadrilateral and hexahedral grids that reduce to cell-based pressure systems. The methods are based on a new family of mixed…
We propose a mixed finite element method for Stokes flow with one degree of freedom per element and facet of simplicial grids. The method is derived by considering the vorticity-velocity-pressure formulation and eliminating the vorticity…
In the presence of strong heterogeneities, it is well known that the use of explicit schemes for the transport of species in a porous medium suffers from severe restrictions on the time step. This has led to the development of implicit…
We develop a cut finite element method for the Darcy problem on surfaces. The cut finite element method is based on embedding the surface in a three dimensional finite element mesh and using finite element spaces defined on the three…
A variational method is presented for directly finding the bifurcation point of nonlinear equations as the saddle-node point of the extended nonlinear Rayleigh quotient. The method is applied for solving an open problem on the existence of…
We study mixed finite element methods for the rotating shallow water equations with linearized momentum terms but nonlinear drag. By means of an equivalent second-order formulation, we prove long-time stability of the system without energy…
Decentralized optimization methods have been in the focus of optimization community due to their scalability, increasing popularity of parallel algorithms and many applications. In this work, we study saddle point problems of sum type,…
We develop a numerical scheme for a two-phase immiscible flow in heterogeneous porous media using a structured grid finite element method, which have been successfully used for the computation of various physical applications involving…
We consider a standard elliptic partial differential equation and propose a geometric multigrid algorithm based on Dirichlet-to-Neumann (DtN) maps for hybridized high-order finite element methods. The proposed unified approach is applicable…
In the flow and transport numerical simulation, mesh adaptivity strategy is important in reducing the usage of CPU time and memory. The refinement based on the pressure error estimator is commonly-used approach without considering the flux…
We consider in this paper, a new a posteriori residual type error estimator of a conforming mixed finite element method for the coupling of fluid flow with porous media flow on isotropic meshes. Flows are governed by the Navier-Stokes and…
We present a mixed finite element method for a five-field formulation of the Biot system of poroelasticity that reduces to a cell-centered pressure-displacement system on simplicial and quadrilateral grids. A mixed…
This paper focuses on the distributed optimization of stochastic saddle point problems. The first part of the paper is devoted to lower bounds for the centralized and decentralized distributed methods for smooth (strongly) convex-(strongly)…
This paper explores the application of the multiscale finite element method (MsFEM) to address steady-state Stokes-Darcy problems with BJS interface conditions in highly heterogeneous porous media. We assume the existence of multiscale…
In this work, we propose and computationally investigate a monolithic space-time multirate scheme for coupled problems. The novelty lies in the monolithic formulation of the multirate approach as this requires a careful design of the…
The dual formulation for linear elasticity, in contrast to the primal formulation, is not affected by locking, as it is based on the stresses as main unknowns. Thus it is quite attractive for nearly incompressible and incompressible…
The main focus of this paper is the study of efficient multigrid methods for large linear systems with a particular saddle-point structure. Indeed, when the system matrix is symmetric, but indefinite, the variational convergence theory that…
A modification of the saddle point method is proposed for computation of non-stationary wave processes (pulses) in waveguides. The dispersion diagram of the waveguide is continued analytically. A set of possible saddle points on the…