Stability of Discontinuous Galerkin Spectral Element Schemes for Wave Propagation when the Coefficient Matrices have Jumps.

We use the behavior of the L 2 norm of the solutions of linear hyperbolic equations with discontinuous coefficient matrices as a surrogate to infer stability of discontinuous Galerkin spectral element methods (DGSEM). Although the L 2 norm is not bounded in terms of the initial data for homogeneous and dissipative boundary conditions for such systems, the L 2 norm is easier to work with than a norm that discounts growth due to the discontinuities. We show that the DGSEM with an upwind numerical flux that satisfies the Rankine-Hugoniot (or conservation) condition has the same energy bound as the partial differential equation does in the L 2 norm, plus an added dissipation that depends on how much the approximate solution fails to satisfy the Rankine-Hugoniot jump.

Reoperations and postoperative complications after osteosynthesis of phalangeal fractures: a retrospective cohort study.

OBJECTIVES: The aim of the study was to describe the reoperation rates and postoperative complications associated with different methods of osteosynthesis in all extra-articular, closed fractures of the proximal and middle phalanges operated on in the Department of Hand Surgery at Södersjukhuset beween 2010-2014, and to describe the associated patient demographics. PATIENTS AND METHODS: This study included all the relevant operations, which comprised operations on 181 fractures in 159 patients (82 male, 77 female), median and mean age = 43 (range = 14-88 years). The clinical records and radiographs were examined retrospectively. A logistic regression analysis was performed on the reoperation data to determine which method of osteosynthesis was the most important descriptor for reoperation, and whether the fracture type was a significant confounder. RESULTS: Forty-seven patients (26%) were reoperated on, mainly due to finger stiffness. The reoperation rates were 25% after K-wire, 15% after screws, and 42% after plate fixation. The unadjusted reoperation rate after plate fixation was significantly higher than for the other methods, but not after adjustment for fracture complexity. The proximal phalanx was affected in 88% of the fractures, and 77% were located in the fourth or fifth finger. Falls, animal-related, and sports injuries were the most frequent causes of injuries. CONCLUSION: Open reduction with plate fixation was associated with a higher reoperation rate, but this method was also used for the more complex fractures. Plate fixation for phalangeal fractures often entails a need for later tenolysis and plate removal. More aggressive mobilisation regimes might be indicated to prevent adhesion problems.