Bernstein-Bézier Galerkin-Characteristics Finite Element Method for Convection-Diffusion Problems

نویسندگان

چکیده

Abstract A class of Bernstein-Bézier basis based high-order finite element methods is developed for the Galerkin-characteristics solution convection-diffusion problems. The formulation derived using a semi-Lagrangian discretization total derivative in considered spatial performed method on unstructured meshes. Lagrangian interpretation this approach greatly reduces time truncation errors Eulerian methods. To achieve accuracy solver, requires interpolating procedures. In present work, step carried out functions to evaluate at departure points. Triangular patches are constructed simple and inherent manner over elements along characteristics. An efficient preconditioned conjugate gradient solver used linear systems algebraic equations. Several numerical examples including advection-diffusion equations with known analytical solutions viscous Burgers problem illustrate accuracy, robustness performance proposed approach. computed results support our expectations stable highly accurate

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Finite Element Methods for Convection Diffusion Equation

This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...

متن کامل

Galerkin Characteristics Method for Convection-diffusion Problems with Memory Terms

(1.1) ∂tb(x, u) + div(F̄ (t, x, u)− k∇u) = f(t, x, u, s), s(t, x) = ∫ t 0 K(t, z)ψ(u(z, x))dz in Ω × (0, T ], T < ∞, Ω ⊂ R is a bounded domain, ∂Ω ∈ C, see [26]. If Ω is convex, then ∂Ω is assumed to be Lipschitz continuous. We consider a Dirichlet boundary condition (1.2) u(t, x) = 0 on I × ∂Ω, I = (0, T ], together with the initial condition (1.3) u(0, x) = u0(x) x ∈ Ω. We assume 0 < ε ≤ ∂sb(x...

متن کامل

A Mixed-Hybrid-Discontinuous Galerkin Finite Element Method for Convection-Diffusion Problems

We propose and analyse a new finite element method for convection diffusion problems based on the combination of a mixed method for the elliptic and a discontinuous Galerkin method for the hyperbolic part of the problem. The two methods are made compatible via hybridization and the combination of both is appropriate for the solution of intermediate convection-diffusion problems. By construction...

متن کامل

A hybrid mixed discontinuous Galerkin finite-element method for convection–diffusion problems

We propose and analyse a new finite-element method for convection–diffusion problems based on the combination of a mixed method for the elliptic and a discontinuous Galerkin (DG) method for the hyperbolic part of the problem. The two methods are made compatible via hybridization and the combination of both is appropriate for the solution of intermediate convection–diffusion problems. By constru...

متن کامل

Taylor-Galerkin-based spectral element methods for convection-diffusion problems

• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Scientific Computing

سال: 2022

ISSN: ['1573-7691', '0885-7474']

DOI: https://doi.org/10.1007/s10915-022-01888-7