This paper concerns the superconvergence property of the ultraweak-local discontinuous Galerkin(UWLDG)method for one-dimensional linear sixth-order equations.The crucial technique is the construction of a special proj...This paper concerns the superconvergence property of the ultraweak-local discontinuous Galerkin(UWLDG)method for one-dimensional linear sixth-order equations.The crucial technique is the construction of a special projection.We will discuss in three different situations according to the remainder of k,the highest degree of polynomials in the function space,divided by 3.We can prove the(2k-1)th-order superconvergence for the cell averages when k=0 or 2(mod 3).But if k=1(mod 3),we can only prove a(2k-2)th-order superconvergence.The same superconvergence orders can also be gained for the errors of numerical fuxes.We will also prove the superconvergence of order k+2 at some special quadrature points.Some numerical examples are given at the end of this paper.展开更多
文摘This paper concerns the superconvergence property of the ultraweak-local discontinuous Galerkin(UWLDG)method for one-dimensional linear sixth-order equations.The crucial technique is the construction of a special projection.We will discuss in three different situations according to the remainder of k,the highest degree of polynomials in the function space,divided by 3.We can prove the(2k-1)th-order superconvergence for the cell averages when k=0 or 2(mod 3).But if k=1(mod 3),we can only prove a(2k-2)th-order superconvergence.The same superconvergence orders can also be gained for the errors of numerical fuxes.We will also prove the superconvergence of order k+2 at some special quadrature points.Some numerical examples are given at the end of this paper.
