A space-time adaptive discontinuous Galerkin method for the numerical solution of the dynamic quasi-static von Kármán equations

DOI10.1016/j.camwa.2022.12.005OpenAlexW4312057135MaRDI QIDQ2682669

Ronald H. W. Hoppe

Publication date: 1 February 2023

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2022.12.005

zbMATH Keywords

von Kármán equationsa posteriori error estimationequilibration\(\mathrm{C}^0\) interior penalty discontinuous Galerkin approximation

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Plates (74K20) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Uses Software

• NewtonLib

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An adaptive Newton continuation strategy for the fully implicit finite element immersed boundary method
• Mathematical aspects of discontinuous Galerkin methods.
• An introduction to Sobolev spaces and interpolation spaces
• Solvability of the von Kármán equations with nonhomogeneous boundary conditions in nonsmooth domains
• A posteriori estimates for partial differential equations
• Equilibrated residual error estimates are \(p\)-robust
• A mixed finite element method for the solutions of the von Kármán equations
• Global existence versus blow-up results for a fourth order parabolic PDE involving the Hessian
• Numerical simulation of the formation of spherulites in polycrystalline binary mixtures
• An existence theorem for the von Kármán equations
• A Nonconforming Finite Element Approximation for the von Karman equations
• An Equilibrated A Posteriori Error Estimator for the Interior Penalty Discontinuous Galerkin Method
• An a posteriori error indicator for discontinuous Galerkin approximations of fourth-order elliptic problems
• Von Karman Evolution Equations
• The Stability in L p and W p 1 of the L 2 -Projection onto Finite Element Function Spaces
• A family of $C^1$ finite elements with optimal approximation properties for various Galerkin methods for 2nd and 4th order problems
• Mixed and Hybrid Finite Element Methods
• Finite element approximations of the von Kármán equations
• Error estimates for the numerical approximation of a distributed optimal control problem governed by the von Kármán equations
• A Convergent Adaptive Algorithm for Poisson’s Equation
• A posteriori error estimation for variational problems with uniformly convex functionals
• A C⁰ Interior Penalty Discontinuous Galerkin Method and an equilibrated a posteriori error estimator for a nonlinear fourth order elliptic boundary value problem of p-biharmonic type
• Error control and adaptivity for a variational model problem defined on functions of bounded variation
• A Splitting Scheme for the Numerical Solution of the KWC System
• Adaptive Morley FEM for the von Kármán Equations with Optimal Convergence Rates
• Numerical solution of a phase field model for polycrystallization processes in binary mixtures

This page was built for publication: A space-time adaptive discontinuous Galerkin method for the numerical solution of the dynamic quasi-static von Kármán equations