Related papers: A Cut Finite Element Method for Elliptic Bulk Prob…
A finite element formulation is developed for a poroelastic medium consisting of an incompressible hyperelastic skeleton saturated by an incompressible fluid. The governing equations stem from mixture theory and the application is motivated…
The discrete fracture model (DFM) has been widely used in the simulation of fluid flow in fractured porous media. Traditional DFM uses the so-called hybrid-dimensional approach to treat fractures explicitly as low-dimensional entries (e.g.…
We investigate multiscale finite element methods for an elliptic distributed optimal control problem with rough coefficients. They are based on the (local) orthogonal decomposition methodology of M\aa lqvist and Peterseim.
We propose an unfitted finite element method for numerically solving the time-harmonic Maxwell equations on a smooth domain. The model problem involves a Lagrangian multiplier to relax the divergence constraint of the vector unknown. The…
We present a finite element approach for diffusion problems with thermal fluctuations based on a fluctuating hydrodynamics model. The governing transport equations are stochastic partial differential equations with a fluctuating forcing…
In this paper, we consider multipoint flux mixed finite element discretizations for slightly compressible Darcy flow in porous media. The methods are formulated on general meshes composed of triangles, quadrilaterals, tetrahedra or…
The last decade has seen a strong increase of research into flows in fractured porous media, mainly related to subsurface processes, but also in materials science and biological applications. Connected fractures totally dominate…
A moving mesh finite element method is studied for the numerical solution of Bernoulli free boundary problems. The method is based on the pseudo-transient continuation with which a moving boundary problem is constructed and its steady-state…
Optimally convergent (with respect to the regularity) quadratic finite element method for two dimensional obstacle problem on simplicial meshes is studied in (Brezzi, Hager, Raviart, Numer. Math, 28:431--443, 1977). There was no analogue of…
The phase field model is a widely used mathematical approach for describing crack propagation in continuum damage fractures. In the context of phase field fracture simulations, adaptive finite element methods (AFEM) are often employed to…
We develop a high order cut finite element method for the Stokes problem based on general inf-sup stable finite element spaces. We focus in particular on composite meshes consisting of one mesh that overlaps another. The method is based on…
The paper introduces an adaptive version of the stabilized Trace Finite Element Method (TraceFEM) designed to solve low-regularity elliptic problems on level-set surfaces using a shape-regular bulk mesh in the embedding space. Two…
A high order cut finite element method is formulated for solving the elastic wave equation. Both a single domain problem and an interface problem are treated. The boundary or interface are allowed to cut through the background mesh. To…
This paper presents a new parameter free partially penalized immersed finite element method and convergence analysis for solving second order elliptic interface problems. A lifting operator is introduced on interface edges to ensure the…
The Richards equation, a nonlinear elliptic parabolic equation, is widely used to model infiltration in porous media. We develop a finite element method for solving the Richards equation by introducing a new bounded auxiliary variable to…
We consider a poroelastic medium with a thin heterogeneity, also referred to as a fracture. Fluid flow and mechanical deformation inside both bulk and fracture are governed by the quasi-static Biot equations. The fracture's material…
We investigate the existence, uniqueness, and $L^1$-contractivity of weak solutions to a porous medium equation with fractional diffusion on an evolving hypersurface. To settle the existence, we reformulate the equation as a local problem…
In this paper, we develop a multiscale model reduction technique that describes shale gas transport in fractured media. Due to the pore-scale heterogeneities and processes, we use upscaled models to describe the matrix. We follow our…
The favored phase field method (PFM) has encountered challenges in the finite strain fracture modeling of nearly or truly incompressible hyperelastic materials. We identified that the underlying cause lies in the innate contradiction…
This paper presents an optimum technique based on the least squares method for the derivation of the bubble functions to enrich the standard linear finite elements employed in the formulation of Galerkin weighted-residual statements. The…