A flux‐based HDG method
Copyright policy )A flux‐based HDG method
AbstractIn this article, 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 letting a stabilization parameter tend to infinity. Assuming an inf‐sup condition, we prove its well‐posedness and error estimates of optimal order. We show that the inf‐sup condition is satisfied by some triangular elements. Numerical results are also provided to support our theoretical results.
- University of Tsukuba Japan
- Waseda University Japan
Error bounds for boundary value problems involving PDEs, FOS: Mathematics, Existence problems for PDEs: global existence, local existence, non-existence, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, discontinuous Galerkin method, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, hybridization, error analysis
Error bounds for boundary value problems involving PDEs, FOS: Mathematics, Existence problems for PDEs: global existence, local existence, non-existence, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, discontinuous Galerkin method, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for boundary value problems involving PDEs, hybridization, error analysis
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