相关论文: Adaptive Finite Element Solution of the Porous Med…
An adaptive moving mesh finite element method is studied for the numerical solution of the porous medium equation with and without variable exponents and absorption. The method is based on the so-called moving mesh partial differential…
An adaptive moving mesh finite element method is proposed for the numerical solution of the regularized long wave (RLW) equation. A moving mesh strategy based on the so-called moving mesh PDE is used to adaptively move the mesh to improve…
In this article we present a goal-oriented adaptive finite element method for a class of subsurface flow problems in porous media, which exhibit seepage faces. We focus on a representative case of the steady state flows governed by a…
We present a one-dimensional high-order moving-mesh finite element method for moving boundary problems where the boundary velocity depends implicitly on the solution in the interior of the domain. The method employs a conservative arbitrary…
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…
The paper develops an unfitted finite element method for solving the Darcy system of equations posed in a network of fractures embedded in a porous matrix. The approach builds on the Hughes--Masud stabilized formulation of the Darcy problem…
In this paper we consider modifications to Darcy's equation wherein the drag coefficient is a function of pressure, which is a realistic model for technological applications like enhanced oil recovery and geological carbon sequestration. We…
We construct a finite element method for the numerical solution of a fractional porous medium equation on a bounded open Lipschitz polytopal domain $\Omega \subset \mathbb{R}^{d}$, where $d = 2$ or $3$. The pressure in the model is defined…
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…
We introduce a framework for the design of finite element methods for two-dimensional moving boundary problems with prescribed boundary evolution that have arbitrarily high order of accuracy, both in space and in time. At the core of our…
We study a nonlocal diffusion equation of porous medium type featuring a generalised fractional pressure with spatial anisotropy. We construct a finite element method for the numerical solution of the equation on a bounded open Lipschitz…
We develop an unfitted compatible finite element discretisation for the Darcy problem based on $H(\mathrm{div})$-conforming flux spaces and discontinuous pressure spaces. The method is designed to preserve pointwise discrete mass…
Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes…
In this paper, we introduce a new approach to solving the porous medium equation using a moving mesh finite element method that leverages the Onsager variational principle as an approximation tool. Both the continuous and discrete problems…
In various applications, design problems involving structures and compliant mechanisms experience fluidic pressure loads. During topology optimization of such design problems, these loads adapt their direction and location with the…
An adaptive moving mesh finite difference method is presented to solve two types of equations with dynamic capillary pressure term in porous media. One is the non-equilibrium Richards Equation and the other is the modified Buckley-Leverett…
We study numerical methods for porous media equation (PME). There are two important characteristics: the finite speed propagation of the free boundary and the potential waiting time, which make the problem not easy to handle. Based on…
This work proposes a nonlinear finite element method whose nodal values preserve bounds known for the exact solution. The discrete problem involves a nonlinear projection operator mapping arbitrary nodal values into bound-preserving ones…
The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. An energetic variational approach has been studied in a recent work [6], in which the trajectory equation is obtained, and a few first order accurate…
Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…