An hp-version of the C^0-continuous Petrov-Galerkin method for second-order Volterra integro-differential equations
An hp-version of the C^0-continuous Petrov-Galerkin method for second-order Volterra integro-differential equations
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二阶 Volterra 积分微分方程的 C^0 连续 Petrov-Galerkin 方法的 hp 版本
DOI：
10.1016/j.apnum.2020.01.017
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发表时间：
2020
影响因子：
2.8
通讯作者：
Lijun Yi
中科院分区：
文献类型：
--
作者：
Shuangshuang Li;Lina Wang;Lijun Yi
提出了一种求解二阶线性沃尔泰拉积分微分方程的C 0连续Petrov-Galerkin方法的hp-版本.我们结合联合收割机的连续和不连续的伽辽金方法，以获得一个自然的离散化的二阶导数的任意阶。我们推导出先验误差界的L2-和H1-范数是完全明确的当地时间步长，当地的逼近阶，和当地的正则性的精确解。数值实验验证了理论结果。
We present an hp-version of the C 0-continuous Petrov-Galerkin method for linear second-order Volterra integro-differential equations. We combine the continuous and discontinuous Galerkin methodologies to obtain a natural discretization of the second-order derivative of arbitrary order. We derive a-priori error bounds in the L 2-and H 1-norm that are completely explicit in the local time steps, local approximation orders, and local regularity of the exact solution. Numerical experiments are provided to illustrate the theoretical results.