In this article, two sets of fourth-order compact finite difference schemes are constructed for solving heatconducting problems of two or three dimensions, respectively. Both problems are with Neumann boundary conditions. These works are extensions of our earlier work (Zhao et al., Fourth order compact schemes of a heat conduction problemwith Neumann boundary conditions, NumericalMethods Partia...

Over a perfect field k of characteristic p > 0, we construct a “Witt vector cohomology with compact supports” for separated k-schemes of finite type, extending (after tensorisation with Q) the classical theory for proper k-schemes. We define a canonical morphism from rigid cohomology with compact supports to Witt vector cohomology with compact supports, and we prove that it provides an identifi...

The Laboratory's main facility is outside Chicago, at 9700 South Cass Avenue, Argonne, Illinois 60439. For information about Argonne and its pioneering science and technology programs, see www.anl.gov. Solutions to hyperbolic conservation laws are often characterized by a large range of length scales as well as discontinuities. Standard nonlinear finite-difference schemes, such as the WENO sche...

The Laboratory's main facility is outside Chicago, at 9700 South Cass Avenue, Argonne, Illinois 60439. For information about Argonne and its pioneering science and technology programs, see www.anl.gov. Solutions to hyperbolic conservation laws are often characterized by a large range of length scales as well as discontinuities. Standard nonlinear finite-difference schemes, such as the WENO sche...