H (div) approximations based on hp-adaptive curved meshes using quarter point elements

Denise de Siqueira, Agnaldo Farias, Philippe Devloo, Sônia Gomes


H(div)-conforming finite element subspaces based on curved quadrilateral meshes, with hp-adaptation, are constructed to be applied in flux approximations of the mixed element formulation. In order to validate the implementation, a test problem with square-root singularity at a boundary point is simulated. The results demonstrate exponential rates of convergence, and a dramatic error reduction when quarter-point elements are applied close to the singularity. Using static condensation, the global condensed matrices to be solved have reduced dimension, which is proportional to the dimension of border fluxes.


H(div) finite element space, hp adaptivity, curves elements.

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DOI: https://doi.org/10.5540/03.2017.005.01.0314


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