Finite volume element method with the WSGD formula for nonlinear fractional mobile/immobile transport equations

Finite Element Method for Linear Multiterm Fractional Differential Equations

A Finite Element Method for Time Fractional Partial Differential Equations

In this paper, we consider the finite element method for time fractional partial differential equations. The existence and uniqueness of the solutions are proved by using the Lax-Milgram Lemma. A time stepping method is introduced based on a quadrature formula approach. The fully discrete scheme is considered by using a finite element method and optimal convergence error estimates are obtained....

Finite Volume Element Method for Second Order Hyperbolic Equations

We discuss a priori error estimates for a semidiscrete piecewise linear finite volume element (FVE) approximation to a second order wave equation in a two-dimensional convex polygonal domain. Since the domain is convex polygonal, a special attention has been paid to the limited regularity of the exact solution. Optimal error estimates in L2, H1 norms and quasioptimal estimates in L∞ norm are di...

A Finite Volume Element Method for a Nonlinear Parabolic Problem

We study a finite volume element discretization of a nonlinear parabolic equation in a convex polygonal domain. We show existence of the discrete solution and derive error estimates in L2– and H –norms. We also consider a linearized method and provide numerical results to illustrate our theoretical findings.

A Mixed Finite Element Method for Nonlinear Diffusion Equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as ...