PP 1748/2: Foundation and Application of Generalized Mixed FEM Towards Nonlinear Problems in Solid Mechanics
The research of this project aims at the mathematical foundation and the engineering application of generalized mixed FEM as well as the development and the analysis of new non-standard methods that yield guaranteed results for nonlinear problems in solid mechanics. The workgroup will continue their analysis on nonlinear problems in raising difficulty from Hencky material to polyconvex material and geometric nonlinear configurations. Recent breakthroughs in the dPG methodology for nonlinear problems motivate the application of adaptive dPG schemes with built-in error control to further problems such as hyperelasticity, the obstacle problem and time-evolving elastoplasticity. Optimal convergence rates of adaptive nonlinear LS and dPG methods and Arnold-Winther FEM and guaranteed error estimation for dPG methods involving explicit constants and correct scaling will be investigated.
Financer
Duration of project
Start date: 10/2018
End date: 03/2023
Research Areas
Publications
C. Carstensen. Collective marking for adaptive least-squares finite element methods with optimal rates. Math. Comp., 89(321):89–103, 2020.
C. Carstensen, A. K. Dond, and H. Rabus. Quasi-optimality of adaptive mixed FEMs for non-selfadjoint indefinite second-order linear elliptic problems. Comput. Methods Appl. Math., 19(2):233–250, 2019.
C. Carstensen, D. Gallistl, and J. Gedicke. Residual-based a posteriori error analysis for symmetric mixed Arnold-Winther FEM. Numer. Math., 142(2):205–234, 2019.
C. Carstensen, D. Liu, and J. Alberty. Convergence of dG(1) in elastoplastic evolution. Numer. Math., 141(3):715–742, 2019.
C. Carstensen, G. Mallik, and N. Nataraj. A priori and a posteriori error control of discontinuous Galerkin finite element methods for the von Kármán equations. IMA J. Numer. Anal., 39(1):167–200, 2019.
Carsten Carstensen and Sophie Puttkammer. How to prove the discrete reliability for nonconforming finite element methods. J. Comput. Math., 38(1):142–175, 2020.
