An explicit scheme for time-dependent convection-diffusion problems is presented. It is shown that convenient bounds for the time step value ensureL∞ stability, in both space and time, for piecewise linear finite element discretizations in any space dimension. Convergence results in the same sense are also demonstrated under certain conditions. Numerical results certify the good performance of the scheme.

中文翻译：

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对流-扩散方程的一种显式方法

提出了一个时间相关的对流扩散问题的明确方案。结果表明，对于任何空间维度中的分段线性有限元离散化，时间步长值的方便界限确保了空间和时间上的 L∞ 稳定性。在某些条件下也证明了相同意义上的收敛结果。数值结果证明了该方案的良好性能。