No abstract

The least-squares Legendre and Chebyshev pseudospectral methods are presented for a first-order system equivalent to a second-order elliptic partial differential equation. Continuous and discrete homogeneous least-squares functionals using Legendre and Chebyshev weights are shown to be equivalent to the H 1 (Ω) norm and Chebyshev-weighted Div-Curl norm over appropriate polynomial spaces, respectively. The spectral error estimates are derived. The block diagonal finite element preconditioner is developed for the both cases. Several numerical tests are demonstrated on the spectral discretization errors and on performances of the finite element preconditioner.

Spontaneous retroperitoneal hemorrhage is one of the most serious and often lethal complications of anticoagulation therapy. The clinical symptoms vary from femoral neuropathy to abdominal compartment syndrome or fatal hypovolemic shock. Of these symptoms, abdominal compartment syndrome is the most serious of all, because it leads to anuria, worsening of renal failure, a decrease in cardiac output, respiratory failure, and intestinal ischemia. We report a case of a spontaneous retroperitoneal hemorrhage in a 48-year-old female who had been receiving warfarin and aspirin for her artificial aortic valve. She presented with a sudden onset of lower abdominal pain, dizziness and a palpable abdominal mass after prolonged straining to defecate. Computed tomography demonstrated a huge retroperitoneal hematoma and active bleeding from the right internal iliac artery. After achieving successful bleeding control with transcatheter arterial embolization, surgical decompression of the hematoma was performed for management of the femoral neuropathy and the abdominal compartment syndrome. She recovered without any complications. We suggest that initial hemostasis by transcatheter arterial embolization followed by surgical decompression of hematoma is a safe, effective treatment method for a spontaneous retroperitoneal hemorrhage complicated with intractable pain, femoral neuropathy, or abdominal compartment syndrome.

a b s t r a c tIn this paper, we propose some least-squares finite element procedures for linear and nonlinear parabolic equations based on first-order systems. By selecting the least-squares functional properly each proposed procedure can be split into two independent symmetric positive definite sub-procedures, one of which is for the primary unknown variable u and the other is for the expanded flux unknown variable σ . Optimal order error estimates are developed. Finally we give some numerical examples which are in good agreement with the theoretical analysis.