In this paper, we study the superconvergence of the error between the discontinuous Galerkin (DG) finite element solution and the exact solution for linear conservation laws when upwind fluxes are used. We prove that if we apply piecewise k-th degree polynomials, the error between the DG solution and the exact solution is (k + 2)-th order superconvergent at… (More)
In this paper, several definitions for generalized convexity and generalized monotonicity are introduced, and the relationships between a generalized vector equilibrium problem and its dual problem for these generalized convex and generalized monotone mappings are considered. By making use of Nadler's Lemma and the fixed point theorem of set-valued mapping,… (More)
We obtain a Struwe type global compactness result for a class of nonlinear nonlocal problems involving the fractional p−Laplacian operator and nonlinearities at critical growth.
We obtain nontrivial solutions to the Brezis-Nirenberg problem for the fractional p-Laplacian operator, extending some results in the literature for the fractional Lapla-cian. The quasilinear case presents two serious new difficulties. First an explicit formula for a minimizer in the fractional Sobolev inequality is not available when p = 2. We get around… (More)
In this paper, we study the superconvergence of the error for the local discontinuous Galerkin (LDG) finite element method for one-dimensional linear parabolic equations when alternating flux is used. We prove that if we apply piecewise k-th degree polynomials, the error between the LDG solution and the exact solution is (k + 2)-th order superconvergent at… (More)