Related papers: A Multigrid Method for a Nitsche-based Extended Fi…
This paper investigates energy-minimization finite-element approaches for the computation of nematic liquid crystal equilibrium configurations. We compare the performance of these methods when the necessary unit-length constraint is…
A multiscale optimization framework for problems over a space of Lipschitz continuous functions is developed. The method solves a coarse-grid discretization followed by linear interpolation to warm-start project gradient descent on…
Many subsurface engineering applications involve tight-coupling between fluid flow, solid deformation, fracturing, and similar processes. To better understand the complex interplay of different governing equations, and therefore design…
We propose an unfitted interface penalty Discontinuous Galerkin-Finite Element Method (UIPDG-FEM) for elliptic interface problems. This hybrid method combines the interior penalty discontinuous Galerkin (IPDG) terms near the…
We establish the existence theory of several commonly used finite element (FE) nonlinear fully discrete solutions, and the convergence theory of a linearized iteration. First, it is shown for standard FE, SUPG and edge-averaged method…
Interfacial energy plays an important role in equilibrium morphologies of nanosized microstructures of solid materials due to the high interface-to-volume ratio, and can no longer be neglected as it does in conventional mechanics analysis.…
In this paper, we consider a poroelasticity problem in heterogeneous multicontinuum media that is widely used in simulations of the unconventional hydrocarbon reservoirs and geothermal fields. Mathematical model contains a coupled system of…
In this paper, we propose a multiscale method for the Darcy-Forchheimer model in highly heterogeneous porous media. The problem is solved in the framework of generalized multiscale finite element methods (GMsFEM) combined with a multipoint…
This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of…
Unfitted finite element methods have emerged as a popular alternative to classical finite element methods for the solution of partial differential equations and allow modeling arbitrary geometries without the need for a boundary-conforming…
The performance of finite element solvers on modern computer architectures is typically memory bound for sufficiently large problems. The main cause for this is that loading matrix elements from RAM into CPU cache is significantly slower…
We introduce an unfitted Nitsche finite element method with a new ghost-penalty stabilization based on local projection of the solution gradient. The proposed ghost-penalty operator is straightforward to implement, ensures algebraic…
Recent work on octree-based finite-element systems has developed a multigrid solver for Poisson equations on meshes. While the idea of defining a regularly indexed function space has been successfully used in a number of applications, it…
Elliptic interface problems whose solutions are $C^0$ continuous have been well studied over the past two decades. The well-known numerical methods include the strongly stable generalized finite element method (SGFEM) and immersed FEM…
We construct and analyse a $hp$-FE/BE coupling on non-matching meshes, based on Nitsche's method. Both the mesh size and the polynomial degree are changed to improve accuracy. Nitsche's method leads to a positive definite formulation, thus,…
We show the stability of a penalty-free asymmetric Nitsche's method using N\'ed\'elec edge elements for solving curl-curl-type problems with tangential Dirichlet boundary conditions imposed weakly. The main result is an inf-sup stability…
In this work, we extend the equal-order stabilized scheme discussed in [Franca et al., Comput. Methods Appl. Mech. Engrg. 99 (1992) 209-233] to accommodate slip (i.e., Navier) boundary conditions for the stationary Navier-Stokes equations.…
In this article we consider two-grid finite element methods for solving semilinear interface problems in d space dimensions, for d=2 or d=3. We first describe in some detail the target problem class with discontinuous diffusion…
A two-grid scheme based on mixed finite-element approximations to the incompressible Navier-Stokes equations is introduced and analyzed. In the first level the standard mixed finite-element approximation over a coarse mesh is computed. In…
Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier…