Numerical methods for porous medium equation by an energetic variational approach

Numerical Methods with Interface Estimates for the Porous Medium Equation*

If the data has slightly more regularity, then this too is satisfied by the solution. Specifically, if m is no greater than two and u0 is Lipschitz continuous, then u( · , t) is also Lipschitz; if m is greater than two and (u 0 )x ∈ L(R), then (u( · , t))x ∈ L(R) (see [4]). (This will follow from results presented here, also.) We also use the fact that the solution u is Hölder continuous in t [...

Numerical solution of Klein-Gordon equation by using the Adomian's decomposition and variational iterative methods

Numerical Simulation of Biot-wave equation in porous medium

Xinming Zhang Chaoying Zhou Jiaqi Liu Ke’an Liu 1 Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, China 2 Professor, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, China 3, 4 Professor, Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China Email: [email protected],[email protected] ABSTRACT: In this ...

Numerical Simulation for Porous Medium Equation by Local Discontinuous Galerkin Finite Element Method

In this paper we will consider the simulation of the local discontinuous Galerkin (LDG) finite element method for the porous medium equation (PME), where we present an additional nonnegativity preserving limiter to satisfy the physical nature of the PME. We also prove for the discontinuous P0 finite element that the average in each cell of the LDG solution for the PME maintains nonnegativity if...

numerical solution of klein-gordon equation by using the adomian's decomposition and variational iterative methods