相关论文: An algorithm for one-dimensional Generalized Porou…
In this paper, a parameter-uniform fitted mesh finite difference scheme is constructed and analyzed for a class of singularly perturbed interior turning point problems. The solution of this class of turning point problem possess two outflow…
We consider a zero-range process $\eta^N_t(x)$ with superlinear local jump rate, which in a hydrodynamic-small particle rescaling converges to the porous medium equation $\partial_t u=\frac12\Delta u^\alpha, \alpha>1$. As a main result we…
This papers deals with a construction and convergence analysis of a finite difference scheme for solving time-fractional porous medium equation. The governing equation exhibits both nonlocal and nonlinear behaviour making the numerical…
We consider a porous mediaum flow in which the gas is initially distributed in the exterior of an empty region (a hole) and study the final stage of the hole-filling process. Hole-filling is asymptotically described by a self-similar…
We consider the one-dimensional porous medium equation $u_t=\left (u^nu_x \right )_x+\frac{\mu}{x}u^nu_x$. We derive point transformations of a general class that map this equation into itself or into equations of a similar class. In some…
In this work we are interested in dealing with single-phase flows in fractured porous media for underground processes. We focus our attention on domains where the presence of faults, with thickness several orders of magnitude smaller than…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
We present a novel Eulerian meshless method for two-phase flows with arbitrary embedded geometries. The spatial derivatives are computed using the meshless generalized finite difference method (GFDM). The sharp phase interface is tracked…
We formulate a numerical method to solve the porous medium type equation with fractional diffusion \[ \frac{\partial u}{\partial t}+(-\Delta)^{\sigma/2} (u^m)=0 \] posed for $x\in \mathbb{R}^N$, $t>0$, with $m\geq 1$, $\sigma \in (0,2)$,…
The simulation of certain flow problems requires a means for modeling a free fluid surface; examples being viscoelastic die swell or fluid sloshing in tanks. In a finite-element context, this type of problem can, among many other options,…
We introduce a new scheme for solving the non-regularized Porous Medium Equation. It is mass conserving and uses only positive unknown values. To address these typically conflicting features, we employ the eXtreme Mesh deformation approach…
We use a diffuse interface method for solving Poisson's equation with a Dirichlet condition on an embedded curved interface. The resulting diffuse interface problem is identified as a standard Dirichlet problem on approximating regular…
In this paper, we study the stability and convergence of a decoupled and linearized mixed finite element method (FEM) for incompressible miscible displacement in a porous media whose permeability and porosity are discontinuous across some…
We present a new fixed mesh algorithm for solving a class of interface inverse problems for the typical elliptic interface problems. These interface inverse problems are formulated as shape optimization prob- lems whose objective…
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…
The paper develops a hybrid method for solving a system of advection--diffusion equations in a bulk domain coupled to advection--diffusion equations on an embedded surface. A monotone nonlinear finite volume method for equations posed in…
We introduce and analyze a numerical approximation of the porous medium equation with fractional potential pressure introduced by Caffarelli and V\'azquez: \[ \partial_t u = \nabla \cdot (u^{m-1}\nabla (-\Delta)^{-\sigma}u) \qquad…
We introduce a diffuse interface box method (DIBM) for the numerical approximation on complex geometries of elliptic problems with Dirichlet boundary conditions. We derive a priori $H^1$ and $L^2$ error estimates highlighting the r\^{o}le…
In this paper we are interested with a strongly coupled system of partial differential equations that modelizes free convection in a two-dimensional bounded domain filled with a fluid saturated porous medium. This model is inspired by the…
Given a bounded domain $D \subset \mathbb{R}^N$ and $m > 1$, we study the long-time behaviour of solutions to the Porous Medium equation (PME) posed in a tube \[ \partial_tu = \Delta u^m \quad \text{ in } D \times \mathbb{R}, \quad t > 0,…