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

By Emmanuil H. Georgoulis, Paul Houston, Juha M. Virtanen. 2011

111 citations recorded by the source corpus.

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.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/c36e4b4ac5e936306dd7480168a0bcad652406e1