2021/12/30 by Thomas Führer, Führer, Thomas, Pablo Herrera +3
Computer Science · Engineering · Mathematics · #35J35 #35J67 #65N30 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2112.15153
openalex publication_date 2021/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a fourth-order div problem and its approximation by the discontinuous Petrov-Galerkin method with optimal test functions. We present two variants, based on first and second-order systems. In both cases we prove well-posedness of the formulation and quasi-optimal convergence of the approximation. Our analysis includes the fully-discrete schemes with approximated test functions, for general dimension and polynomial degree in the first-order case, and for two dimensions and lowest-order approximation in the second-order case. Numerical results illustrate the performance for quasi-uniform and adaptively refined meshes.