AI summary · arXiv: 1910.12959v1 · math.NA
Convergence of an adaptive $C^0$-interior penalty Galerkin method for the biharmonic problem
The essentials
- Authors present a convergence analysis for an adaptive C0IPG method applied to the Biharmonic problem
- Convergence without rates is provided for all practically relevant marking strategies and penalty parameters
- Analysis explores embedding properties of (broken) Sobolev and BV spaces, and constructs a suitable limit space
- New technical tools are developed to address the challenge of Lagrange finite element spaces not containing a proper C1-conforming subspace
- Basic convergence result is established for the adaptive C0IPG method for solving the Biharmonic problem
- Paper contributes to advancing understanding of adaptive numerical methods for PDEs
- Findings have implications for practical applications requiring accurate solutions to biharmonic problems.
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