A Finite Element-Finite Volume Discretization of Convection-Diffusion-Reaction Equations with Nonhomogeneous Mixed Boundary Conditions: Error Estimates

作者：Deuring Paul^*

来源：Numerical Methods for Partial Differential Equations, 2016, 32(6): 1591-1621.

DOI：10.1002/num.22064

• convection-diffusion equation
• combined finite element-finite volume method
• Crouzeix-Raviart finite elements
• barycentric finite volumes
• upwind method
• error estimates

We consider a time-dependent and a steady linear convection-diffusion-reaction equation whose coefficients are nonconstant. Boundary conditions are mixed (Dirichlet and Robin-Neumann) and nonhomogeneous. Both the unsteady and the steady problem are approximately solved by a combined finite element-finite volume method: the diffusion term is discretized by Crouzeix-Raviart piecewise linear finite elements on a triangular grid, and the convection term by upwind barycentric finite volumes. In the unsteady case, the implicit Euler method is used as time discretization. The L-2(H-1) - and the L-infinity(L-2) - error in the unsteady case and the H-1-error in the steady one are estimated against the data, in such a way that no parameter enters exponentially into the constants involved.

• 出版日期2016-11