A priori error analysis of high-order LL* (FOSLL*) finite element methods

Keith, Brendan

doi:10.1016/j.camwa.2021.10.015

Cited by 7 publications

(1 citation statement)

References 41 publications

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“…A Petrov-Galerkin method is then used for the discretization: inspired by [9], we first choose an appropriate test space and then define the (non-standard) trial space to preserve optimal inf-sup stability. After completion of this work, we learned that this approach is very closely related to the DPG * method [13,21].…”

Section: Introductionmentioning

confidence: 99%

An ultraweak space-time variational formulation for the wave equation: Analysis and efficient numerical solution

et al. 2022

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We introduce an ultraweak space-time variational formulation for the wave equation, prove its well-posedness (even in the case of minimal regularity) and optimal inf-sup stability. Then, we introduce a tensor product-style space-time Petrov-Galerkin discretization with optimal discrete inf-sup stability, obtained by a non-standard definition of the trial space. As a consequence, the numerical approximation error is equal to the residual, which is particularly useful for a posteriori error estimation. For the arising discrete linear systems in space and time, we introduce efficient numerical solvers that appropriately exploit the equation structure, either at the preconditioning level or in the approximation phase by using a tailored Galerkin projection. This Galerkin method shows competitive behavior concerning wall-clock time, accuracy and memory as compared with a standard time-stepping method in particular in low regularity cases. Numerical experiments with a 3D (in space) wave equation illustrate our findings.

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Section: Introductionmentioning

confidence: 99%