Weak Galerkin method with implicit θ-schemes for second-order parabolic problems

Qi, Wenya; Song, Lunji

doi:10.1016/j.amc.2019.124731

Applied Mathematics and Computation

2020

DOI: 10.1016/j.amc.2019.124731

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Weak Galerkin method with implicit θ-schemes for second-order parabolic problems

Wenya Qi

Lunji Song

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Cited by 5 publications

(1 citation statement)

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“…In [16], we defined weak double-valued edge functions and adopted elements (P k (T ), P k (e), RT k (T )), for strengthening the flexibility of the WG finite element method and utilizing its numerical solution elementwise belonging to H(div). In this case, the usual stabilization term does not appear.…”

mentioning

confidence: 99%

A new over-penalized weak galerkin finite element method. Part Ⅱ: Elliptic interface problems

Song¹,

Qi²,

Liu³

et al. 2021

DCDS-B

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We introduce an over-penalized weak Galerkin method for elliptic interface problems with non-homogeneous boundary conditions and discontinuous coefficients, where the method combines a weak Galerkin stabilizer with interior penalty terms. This method employs double-valued functions on interior edges of elements instead of single-valued ones and elements (P k , P k , [P k−1 ] 2). As an advantage of the method, elliptic interface problems with low regularity are approximated well. The over-penalized weak Galerkin method is based on weak functions whose edge part is double-valued on each interior edge sharing by two neighboring elements. Jumps between the edge parts are naturally used to define penalty terms. The over-penalized weak Galerkin method allows to use arbitrary meshes, even for low regularity solutions. These features make the new method more flexible and efficient for solving interface equations. Furthermore, a priori error estimates in energy and L 2 norms are derived rigorously, and numerical results confirm the effectiveness of the method.

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mentioning

confidence: 99%

A new over-penalized weak galerkin finite element method. Part Ⅱ: Elliptic interface problems

Song¹,

Qi²,

Liu³

et al. 2021

DCDS-B

Self Cite

View full text Add to dashboard Cite

show abstract

Error analysis of implicit-explicit weak Galerkin finite element method for time-dependent nonlinear convection-diffusion problem

Li,

Gao,

Cui

2025

Applied Numerical Mathematics

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Order Two Superconvergence of the CDG Method for the Stokes Equations on Triangle/Tetrahedron

Ye¹,

Zhang²

2022

jaac

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Weak Galerkin method with implicit θ-schemes for second-order parabolic problems

Cited by 5 publications

References 25 publications

A new over-penalized weak galerkin finite element method. Part Ⅱ: Elliptic interface problems

A new over-penalized weak galerkin finite element method. Part Ⅱ: Elliptic interface problems

Error analysis of implicit-explicit weak Galerkin finite element method for time-dependent nonlinear convection-diffusion problem

Order Two Superconvergence of the CDG Method for the Stokes Equations on Triangle/Tetrahedron

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