We consider goal-oriented adaptive space-time finite-element discretizations of the regularized parabolic p-Laplace problem on completely unstructured simplicial space-time meshes. The adaptivity is driven by the dual-weighted residual (DWR) method since we are interested in an accurate computation of some possibly nonlinear functionals at the solution. Such functionals represent goals in which engineers are often more interested than the solution itself. The DWR method requires the numerical solution of a linear adjoint problem that provides the sensitivities for the mesh refinement. This can be done by means of the same full space-time finite element discretization as used for the primal non-linear problems. The numerical experiments presented demonstrate that this goal-oriented, full space-time finite element solver efficiently provides accurate numerical results for different functionals.

翻译：本文研究了在完全非结构化单纯形时空网格上，针对正则化抛物型p-Laplace问题的目标导向自适应时空有限元离散方法。由于我们对解的一些可能非线性泛函的精确计算感兴趣（这些泛函代表工程师们通常比解本身更关注的目标），自适应过程由对偶加权残量法驱动。该方法需要数值求解一个线性伴随问题，该问题提供网格细化的灵敏度信息。该伴随问题的求解可采用与原始非线性问题相同的全时空有限元离散格式。数值实验表明，该目标导向的全时空有限元求解器能够高效地为不同泛函提供精确的数值结果。