A Posteriori Error Analysis for Implicit-Explicit hp-Discontinuous Galerkin Timestepping Methods for Semilinear Parabolic Problems
A Posteriori Error Analysis for Implicit-Explicit hp-Discontinuous Galerkin Timestepping Methods for Semilinear Parabolic Problems
复制标题
半线性抛物型问题隐式-显式hp-不连续伽辽金时间步长方法的后验误差分析
DOI：
10.1007/s10915-020-01130-2
复制
发表时间：
2020
影响因子：
2.5
通讯作者：
Cangiani A
中科院分区：
文献类型：
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作者：
Cangiani A
一个后验误差估计的和范数的全离散时空方法离散半线性抛物问题，这里表示一个发展偏微分方程问题的Gelfand三元组。特别是，隐式显式变阶（HP版本）不连续Galerkin时间步长计划，在空间中与符合有限元离散。显式处理的非线性反应，而线性空间算子的隐式处理，允许时间推进，而不需要解决每个时间步长的非线性系统。在获得这些误差估计的主要工具是最近的时空重建提出的Georgoulis等人。（一个后验误差界的完全离散的hp-不连续Galerkin时间步进方法的抛物问题，提交出版）的线性抛物问题，这是现在扩展到半线性问题通过非标准的延续参数。一些数值研究也包括突出的最优性提出的后验界。
A posteriorierror estimates in the- and-norms are derived for fully-discrete space–time methods discretising semilinear parabolic problems; heredenotes a Gelfand triple for an evolution partial differential equation problem. In particular, an implicit–explicit variable order (hp-version) discontinuous Galerkin timestepping scheme is employed, in conjunction with conforming finite element discretisation in space. The nonlinear reaction is treated explicitly, while the linear spatial operator is treated implicitly, allowing for time-marching without the need to solve a nonlinear system per timestep. The main tool in obtaining these error estimates is a recent space–time reconstruction proposed in Georgoulis et al. (A posteriori error bounds for fully-discrete hp-discontinuous Galerkin timestepping methods for parabolic problems, Submitted for publication) for linear parabolic problems, which is now extended to semilinear problems via a non-standard continuation argument. Some numerical investigations are also included highlighting the optimality of the proposed a posteriori bounds.