Hybridization of Mixed High-Order Methods on General Meshes and Application to the Stokes Equations
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Joubine Aghili
,
Sébastien Boyaval
Abstract
This paper presents two novel contributions on the recently introduced Mixed High-Order (MHO) methods [`Arbitrary order mixed methods for heterogeneous anisotropic diffusion on general meshes', preprint (2013)]. We first address the hybridization of the MHO method for a scalar diffusion problem and obtain the corresponding primal formulation. Based on the hybridized MHO method, we then design a novel, arbitrary order method for the Stokes problem on general meshes. A full convergence analysis is carried out showing that, when independent polynomials of degree k are used as unknowns (at elements for the pressure and at faces for each velocity component), the energy-norm of the velocity and the L2-norm of the pressure converge with order (k + 1), while the L2-norm of the velocity (super-)converges with order (k + 2). The latter property is not shared by other methods based on a similar choice of unknowns. The theoretical results are numerically validated in two space dimensions on both standard and polygonal meshes.
© 2015 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Hybridization of Mixed High-Order Methods on General Meshes and Application to the Stokes Equations
- Finite Element Analysis of an Exponentially Graded Mesh for Singularly Perturbed Problems
- A Reliable Residual Based A Posteriori Error Estimator for a Quadratic Finite Element Method for the Elliptic Obstacle Problem
- On the Theory of TE Waves Guided by a Lossy Three-Layer Structure with General Nonlinear Permittivity
- Analysis of Model Variance for Ensemble Based Turbulence Modeling
- On the Finite Volume Multigrid Method: Comparison of Intergrid Transfer Operators
- Approximation of Semilinear Fractional Cauchy Problem
- Pointwise Computation in an Ill-Posed Spherical Pseudo-Differential Equation
- On Conditioning of Constraints Arising from Variationally Consistent Discretization of Contact Problems and Duality Based Solvers
- The High Order Method with Discrete TBCs for Solving the Cauchy Problem for the 1D Schrödinger Equation
Artikel in diesem Heft
- Frontmatter
- Hybridization of Mixed High-Order Methods on General Meshes and Application to the Stokes Equations
- Finite Element Analysis of an Exponentially Graded Mesh for Singularly Perturbed Problems
- A Reliable Residual Based A Posteriori Error Estimator for a Quadratic Finite Element Method for the Elliptic Obstacle Problem
- On the Theory of TE Waves Guided by a Lossy Three-Layer Structure with General Nonlinear Permittivity
- Analysis of Model Variance for Ensemble Based Turbulence Modeling
- On the Finite Volume Multigrid Method: Comparison of Intergrid Transfer Operators
- Approximation of Semilinear Fractional Cauchy Problem
- Pointwise Computation in an Ill-Posed Spherical Pseudo-Differential Equation
- On Conditioning of Constraints Arising from Variationally Consistent Discretization of Contact Problems and Duality Based Solvers
- The High Order Method with Discrete TBCs for Solving the Cauchy Problem for the 1D Schrödinger Equation
