A finite element method for time-dependent convection-diffusion equations

Richter, Gerard R.

doi:10.1090/S0025-5718-1990-0993932-9

A finite element method for time-dependent convection-diffusion equations
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Math. Comp. 54 (1990), 81-106 Request permission

Abstract:

We present a finite element method for time-dependent convection-diffusion equations. The method is explicit and is applicable with piecewise polynomials of degree $n \geq 2$. In the limit of zero diffusion, it reduces to a recently analyzed finite element method for hyperbolic equations. Near optimal error estimates are derived. Numerical results are given.

References

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A finite element method for convection-diffusion problems

Triangular mesh methods for the neutron transport equation

Gerard R. Richter, An optimal-order error estimate for the discontinuous Galerkin method, Math. Comp. 50 (1988), no. 181, 75–88. MR 917819, DOI 10.1090/S0025-5718-1988-0917819-3