An expanded mixed covolume method for sobolev equation with convection term on triangular grids

Abstract

The expanded mixed covolume method for the two-dimensional Sobolev equation with convection term is developed and studied. This method uses the lowest-order Raviart-Thomas mixed finite element space as the trial function space. By introducing a transfer operator γ h which maps the trial function space into the test function space and combining expanded mixed finite element with mixed covolume method, the continuousin-time, discrete-in-time expanded mixed covolume schemes are constructed, and optimal error estimates for these schemes are obtained. Numerical results are given to examine the validity and effectiveness of the proposed schemes.

A Mixed Finite Volume Element Method for Time-Fractional Reaction-Diffusion Equations on Triangular Grids

“…According to Reference [40], the above generalized MFVE projection satisfies the following estimates.…”

“…Our aim is to construct an MFVE scheme [36][37][38][39][40][41] by combining the MFE method [42][43][44][45] with the FVE method [46][47][48][49][50][51] to treat the time Caputo fractional reaction-diffusion equation. The MFVE method can not only simultaneously compute several different quantities but also maintain the local conservativity, which is very important in computational fluid dynamics.…”

Analysis of a space–time continuous Galerkin method for convection-dominated Sobolev equations

“…For nonlinear problems, Gu [11] proposes the characteristic finite element (FE) method. For linear problems, Sun and Yang [12,13] propose two finite difference streamline diffusion schemes, Gao and Rui [14] propose the characteristic mixed finite element (MFE) method based on least-squares, Fang and Li [15] propose an expanded mixed covolume method, Zhang and coworkers [16] propose the continuous interior penalty FE method. However, these works either use FE methods or use finite volume element (FVE) methods in spatial direction and use finite differ-ence schemes with first order accuracy or second order accuracy in temporal direction, which often limit the accuracy of time and some of them are conditional convergence.…”