Optimal multilevel adaptive FEM for the Argyris element

Gräßle, Benedikt

doi:10.1016/j.cma.2022.115352

Computer Methods in Applied Mechanics and Engineering

2022

DOI: 10.1016/j.cma.2022.115352

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Optimal multilevel adaptive FEM for the Argyris element

Benedikt Gräßle

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Cited by 3 publications

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Rate-optimal higher-order adaptive conforming FEM for biharmonic eigenvalue problems on polygonal domains

Carstensen,

Gräßle

2024

Computer Methods in Applied Mechanics and Engineering

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Rate-optimal higher-order adaptive conforming FEM for biharmonic eigenvalue problems on polygonal domains

Carstensen,

Gräßle

2024

Computer Methods in Applied Mechanics and Engineering

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Convergence of Adaptive Crouzeix–Raviart and Morley FEM for Distributed Optimal Control Problems

Dond,

Nataraj,

Nayak

2024

Computational Methods in Applied Mathematics

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This article discusses the quasi-optimality of adaptive nonconforming finite element methods for distributed optimal control problems governed by 𝑚-harmonic operators for m = 1 , 2 m=1,2 . A variational discretization approach is employed and the state and adjoint variables are discretized using nonconforming finite elements. Error equivalence results at the continuous and discrete levels lead to a priori and a posteriori error estimates for the optimal control problem. The general axiomatic framework that includes stability, reduction, discrete reliability, and quasi-orthogonality establishes the quasi-optimality. Numerical results demonstrate the theoretically predicted orders of convergence and the efficiency of the adaptive estimator.

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Local parameter selection in the C⁰ interior penalty method for the biharmonic equation

Bringmann,

Carstensen,

Streitberger

2023

Journal of Numerical Mathematics

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The symmetric 0 interior penalty method is one of the most popular discontinuous Galerkin methods for the biharmonic equation. This paper introduces an automatic local selection of the involved stability parameter in terms of the geometry of the underlying triangulation for arbitrary polynomial degrees. The proposed choice ensures a stable discretization with guaranteed discrete ellipticity constant. Numerical evidence for uniform and adaptive mesh-refinement and various polynomial degrees supports the reliability and efficiency of the local parameter selection and recommends this in practice. The approach is documented in 2D for triangles, but the methodology behind can be generalized to higher dimensions, to non-uniform polynomial degrees, and to rectangular discretizations. An appendix presents the realization of our proposed parameter selection in various established finite element software packages. a detailed documentation of C0 interior penalty method in.

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Optimal multilevel adaptive FEM for the Argyris element

Cited by 3 publications

References 21 publications

Rate-optimal higher-order adaptive conforming FEM for biharmonic eigenvalue problems on polygonal domains

Rate-optimal higher-order adaptive conforming FEM for biharmonic eigenvalue problems on polygonal domains

Convergence of Adaptive Crouzeix–Raviart and Morley FEM for Distributed Optimal Control Problems

Local parameter selection in the C⁰ interior penalty method for the biharmonic equation

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Optimal multilevel adaptive FEM for the Argyris element

Cited by 3 publications

References 21 publications

Rate-optimal higher-order adaptive conforming FEM for biharmonic eigenvalue problems on polygonal domains

Rate-optimal higher-order adaptive conforming FEM for biharmonic eigenvalue problems on polygonal domains

Convergence of Adaptive Crouzeix–Raviart and Morley FEM for Distributed Optimal Control Problems

Local parameter selection in the C0 interior penalty method for the biharmonic equation

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Product

Resources

About

Local parameter selection in the C⁰ interior penalty method for the biharmonic equation