An a posteriori error indicator for discontinuous Galerkin approximations of fourth-order elliptic problems

作者：Georgoulis Emmanuil H^*; Houston Paul; Virtanen Juha

来源：IMA Journal of Numerical Analysis, 2011, 31(1): 281-298.

DOI：10.1093/imanum/drp023

• Discontinuous Galerkin methods
• biharmonic problem
• fourth order PDEs
• a posteriori error analysis
• adaptivity

We introduce a residual-based a posteriori error indicator for discontinuous Galerkin discretizations of the biharmonic equation with essential boundary conditions. We show that the indicator is both reliable and efficient with respect to the approximation error measured in terms of a natural energy norm under minimal regularity assumptions. We validate the performance of the indicator within an adaptive mesh refinement procedure and show its asymptotic exactness for a range of test problems.

• 出版日期2011-1