Space-time adaptive methods for the pseudostress formulation of the Stokes problem
Year: 2026
Type: article
Abstract: In this paper, we are concerned with a posteriori error analysis for fully discrete solutions for the pseudostress-velocity formulation of the time dependent Stokes problem including nonhomogeneous mixed boundary conditions. The pseudostress-velocity formulation of the Stokes problem allows Raviart–Thomas finite elements. Piecewise constant discontinuous Galerkin method in time is proposed so that mixed finite element spaces are permitted to change at different time levels. Space-time a posteriori error estimates are derived by exploiting the residual and error representation formula in combination with the Stokes dual problem. Based on these estimates, we propose an adaptive space-time algorithm (ASTA), which includes features such as a space-time mesh change indicator and the separation of space error indicators from time error indicators. Numerical results highlight the superior efficiency of ASTA compared to uniform meshes. Additionally, our algorithm is able to effectively capture the corner singularity of the pressure variable in the backward-facing step flow problem.
Source: Journal of Numerical Mathematics
Authors: Dongho Kim, Eun-Jae Park, Boyoon Seo
Institution: Yonsei University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,712
OpenAlex ID: W7160714548