A systematic study on weak Galerkin finite element method for second‐order parabolic problems - Deka, Bhupen; Kumar, Naresh (Numerical methods for partial differential equations, 2023)
In the present work, we have described a systematic numerical study on weak Galerkin (WG) finite element method for second‐order linear parabolic problems by allowing polynomial approximations with various degrees for each local element. Convergence of both semidiscrete and fully discrete WG solutions are established in L∞L2$$ L^{∞}\left(L^2\right) $$ and L∞H1$$ L^{∞}\left(H^1\right) $$ norms for a general WG element 𝒫k(K),𝒫j(∂K),𝒫l(K)2, where k≥1$$ k\ge 1 $$, j≥0$$ j\ge 0 $$ and l≥0$$ l\ge 0 $$ are arbitrary integers. The fully discrete space–time discretization is based on a first order in time Euler scheme. Numerical experiments are reported to justify the robustness, reliability and accuracy of the WG finite element method.