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A non-overlapping Schwarz algorithm for the HDG method
Issei Oikawa
In this paper, we present two non-overlapping Schwarz algorithms for the hybridizable discontinuous Galerkin (HDG) method. The first algorithm is based on the Neumann-Neumann metho…
A flux-based HDG method
Issei Oikawa
In this paper, we present a flux-based formulation of the hybridizable discontinuous Galerkin (HDG) method for steady-state diffusion problems and propose a new method derived by l…
Penalty method with Crouzeix-Raviart approximation for the Stokes equations under slip boundary condition
Takahito Kashiwabara, Issei Oikawa, Guanyu Zhou
The Stokes equations subject to non-homogeneous slip boundary conditions are considered in a smooth domain . We propose a finite element scheme bas…
An HDG method with orthogonal projections in facet integrals
Issei Oikawa
We propose and analyze a new hybridizable discontinuous Galerkin (HDG) method for second-order elliptic problems. Our method is obtained by inserting the -orthogonal projectio…
Penalty method with P1/P1 finite element approximation for the Stokes equations under slip boundary condition
Takahito Kashiwabara, Issei Oikawa, Guanyu Zhou
We consider the P1/P1 or P1b/P1 finite element approximations to the Stokes equations in a bounded smooth domain subject to the slip boundary condition. A penalty method is applied…
Analysis of a reduced-order HDG method for the Stokes equations
Issei Oikawa
In this paper, we analyze a hybridized discontinuous Galerkin(HDG) method with reduced stabilization for the Stokes equations. The reduced stabilization enables us to reduce the nu…
A hybridized discontinuous Galerkin method with reduced stabilization
Issei Oikawa
In this paper, we propose a hybridized discontinuous Galerkin(HDG) method with reduced stabilization for the Poisson equation. The reduce stabilization proposed here enables us to…
Hybridized discontinuous Galerkin method for convection-diffusion problems
Issei Oikawa
In this paper, we propose a new hybridized discontinuous Galerkin (DG) method for the convection-diffusion problems with mixed boundary conditions. A feature of the proposed method…
Hybridized Discontinuous Galerkin Method with Lifting Operator
Issei Oikawa
In this paper, we propose a new hybridized discontinuous Galerkin method for the Poisson equation with homogeneous Dirichlet boundary condition. Our method has the advantage that t…