Optimal error estimates for fully discrete Galerkin approximations of semilinear parabolic equations
Optimal error estimates for fully discrete Galerkin approximations of semilinear parabolic equations
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DOI：
10.1051/m2an/2018040
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发表时间：
2017-07
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影响因子：
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通讯作者：
Dominik Meidner;B. Vexler
中科院分区：
文献类型：
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作者：
Dominik Meidner;B. Vexler
本文考虑一类不满足任何增长条件的具有大类非线性项的半线性抛物方程。我们在时间上使用不连续Galerkin格式dG（0）（这是隐式欧拉格式的变体）并在空间上使用协调有限元来离散该问题。本文的主要贡献是证明了离散解的一致有界性。这使我们能够获得关于各种范数的最优误差估计。
We consider a semilinear parabolic equation with a large class of nonlinearities without any growth conditions. We discretize the problem with a discontinuous Galerkin scheme dG(0) in time (which is a variant of the implicit Euler scheme) and with conforming finite elements in space. The main contribution of this paper is the proof of the uniform boundedness of the discrete solution. This allows us to obtain optimal error estimates with respect to various norms.