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- Title
A new over-penalized weak Galerkin method. Part Ⅲ: Convection-diffusion-reaction problems.
- Authors
Wang, Ruiwen; Song, Lunji; Liu, Kaifang
- Abstract
In this paper, we propose an over-penalized weak Galerkin (OPWG) finite element method for stationary convection-diffusion-reaction equations with full variable coefficients. This method employs piecewise polynomial approximations of degree $ k $ ($ k\geq 1 $) for both the scalar function and its trace. Especially, the trace on inter-element boundaries is approximated by double-valued functions instead of single-valued ones. The $ (\mathbb{P}_{k}, \mathbb{P}_{k},[\mathbb{P}_{k-1}]^{d}) $ elements, with dimensions of space $ d = 2,\; 3 $ are employed. Our method deals with the convective term discretized in a trilinear form, and the uniqueness of numerical solutions is discussed. Optimal error estimates in the discrete $ H^1 $-norm and $ L^2 $-norm are established, from which the optimal penalty exponent can be fixed. Numerical examples confirm the theory.
- Subjects
TRANSPORT equation; GALERKIN methods; POLYNOMIAL approximation; FINITE element method; EXPONENTS
- Publication
Discrete & Continuous Dynamical Systems - Series B, 2024, Vol 29, Issue 4, p1
- ISSN
1531-3492
- Publication type
Article
- DOI
10.3934/dcdsb.2023149