Conventional methods of quantum simulation involve trade-offs that limit their applicability to specific contexts where use is optimal. In particular, the interaction picture has been found provide substantial asymptotic advantages for some Hamiltonians, but incurs prohibitive constant factors and incompatible with like qubitization. We a framework allows different be hybridized thereby improve...

<p style='text-indent:20px;'>This paper presents a hybridized weak Galerkin (HWG) finite element method for solving the Brinkman equations. Mathematically, equations can model Stokes and Darcy flows in unified framework so as to describe fluid motion porous media with fractures. Numerical schemes equations, therefore, must be designed tackle at same time. We demonstrate that HWG is capabl...

This paper presents an output-based error estimation and adaptation strategy for hybridized discontinuous Galerkin discretizations of firstand second-order systems of conservation laws. A discrete adjoint solution is obtained by a Schurcomplement solver similar to that used in the primal problem. An error estimate is obtained by computing the adjoint on an enriched solution space that consists ...

We present a systematic and constructive methodology to devise various hybridized discontinuous Galerkin (HDG) methods for linearized shallow water equations. At the heart of our development is an upwind HDG framework obtained by hybridizing the upwind flux in the standard discontinuous Galerkin (DG) approach. The chief idea is to first break the uniqueness of the upwind flux across element bou...