A Crank–Nicolson Finite Volume Element Method for Time Fractional Sobolev Equations on Triangular Grids

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....

Adaptive Finite Volume Method for the Shallow Water Equations on Triangular Grids

This paper presents a numerical entropy production (NEP) scheme for two-dimensional shallow water equations on unstructured triangular grids. We implement NEP as the error indicator for adaptive mesh refinement or coarsening in solving the shallow water equations using a finite volumemethod. Numerical simulations show thatNEP is successful to be a refinement/coarsening indicator in the adaptive...

A Vector Finite Element Time-Domain Method for Solving Maxwell's Equations on Unstructured Hexahedral Grids

In this paper the vector finite element time-domain (VFETD) method is derived, analyzed, and validated. The VFETD method uses edge vector finite elements as a basis for the electric field and face vector finite elements as a basis for the magnetic flux density. The Galerkin method is used to convert Maxwell’s equations to a coupled system of ordinary differential equations. The leapfrog method ...

A Mortar Mixed Finite Volume Method for Elliptic Problems on Non-matching Multi-block Triangular Grids

This article presents a mixed finite volume method for solving second-order elliptic equations with Neumann boundary conditions. The computational domains can be decomposed into non-overlapping sub-domains or blocks and the diffusion tensors may be discontinuous across the sub-domain boundaries. We define a conforming triangular partition on each sub-domains independently, and employ the standa...

Finite Element Method for Linear Multiterm Fractional Differential Equations