Convergence analysis of an adaptive interior penalty discontinuous Galerkin method for the biharmonic problem
-
Thomas Fraunholz
and
Malte Peter
Abstract
For the biharmonic problem, we study the convergence of adaptive C0-Interior Penalty Discontinuous Galerkin (C0-IPDG) methods of any polynomial order. We note that C0-IPDG methods for fourth order elliptic boundary value problems have been suggested in [9, 17], whereas residual-type a posteriori error estimators for C0-IPDG methods applied to the biharmonic equation have been developed and analyzed in [8, 18]. Following the convergence analysis of adaptive IPDG methods for second order elliptic problems [6], we prove a contraction property for a weighted sum of the C0-IPDG energy norm of the global discretization error and the estimator. The proof of the contraction property is based on the reliability of the estimator, a quasi-orthogonality result, and an estimator reduction property. Numerical results are given that illustrate the performance of the adaptive C0-IPDG approach.
© 2015 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- A Newton-like method for computing deflating subspaces
- A nonmonotone inexact smoothing Newton-type method for P0-NCP based on a parametric complementarity function
- Convergence analysis of an adaptive interior penalty discontinuous Galerkin method for the biharmonic problem
- Convergence and error estimation of homotopy analysis method for some type of nonlinear and linear integral equations
- Pythagorean-hodograph cycloidal curves
- A relaxed splitting preconditioner for saddle point problems
- On the logarithms of matrices with central symmetry
- On the convergence of Halley’s method for simultaneous computation of polynomial zeros
Articles in the same Issue
- Frontmatter
- A Newton-like method for computing deflating subspaces
- A nonmonotone inexact smoothing Newton-type method for P0-NCP based on a parametric complementarity function
- Convergence analysis of an adaptive interior penalty discontinuous Galerkin method for the biharmonic problem
- Convergence and error estimation of homotopy analysis method for some type of nonlinear and linear integral equations
- Pythagorean-hodograph cycloidal curves
- A relaxed splitting preconditioner for saddle point problems
- On the logarithms of matrices with central symmetry
- On the convergence of Halley’s method for simultaneous computation of polynomial zeros
