论文标题
使用$ hp $ -fem的时空分数抛物线方程进行指数收敛的离散化
An exponentially convergent discretization for space-time fractional parabolic equations using $hp$-FEM
论文作者
论文摘要
我们考虑一个时空分数抛物面问题。结合基于SINC的基于$ HP $ -FEM的基于SINC-二次的方法，在空间中将Riesz-Dunford积分与$ HP $ -FEM相结合，从而为初始边界值问题带有指数收敛的方案，并具有均匀的右侧。对于不均匀的问题，实施了$ hp $ quadrature的方案。我们严格地证明了指数的融合，重点是小型$ t $，这证明了由于数据不兼容而相对于启动奇异性的稳健性。
We consider a space-time fractional parabolic problem. Combining a sinc-quadrature based method for discretizing the Riesz-Dunford integral with $hp$-FEM in space yields an exponentially convergent scheme for the initial boundary value problem with homogeneous right-hand side. For the inhomogeneous problem, an $hp$-quadrature scheme is implemented. We rigorously prove exponential convergence with focus on small times $t$, proving robustness with respect to startup singularities due to data incompatibilities.
