This work is concerned with the development of an adaptive numerical method for semilinear heat flow models featuring a general (possibly) nonlinear reaction term that may cause the solution to blow up in finite time. The fully discrete scheme consists of a high order discontinuous Galerkin (dG) time stepping method and a conforming finite element discretisation (cG) in space. The proposed adaptive procedure is based on rigorously devised conditional a posteriori error bounds in the $L^{\infty}(L^{\infty})$ norm. Numerical experiments complement the theoretical results.
翻译：这项工作涉及为半线性热流模型开发一个适应性数字方法,该方法以一般(可能)非线性反应术语为特点,可能导致在有限时间内爆炸的解决方案。完全离散的系统包括高分级不连续的Galerkin(dG)时间踏脚法和符合空间的有限元素分解(cG)方法。提议的适应程序以严格设计的“$L ⁇ infty}(L ⁇ infty})(L ⁇ infty})美元规范中附带错误的严格条件为基础。数字实验是对理论结果的补充。
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