TY - JOUR
T1 - Weak Galerkin Finite Element Methods for Parabolic Problems with $L^2$ Initial Data
AU - Kumar , Naresh
AU - Deka , Bhupen
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 199
EP - 228
PY - 2023
DA - 2023/01
SN - 20
DO - http://doi.org/10.4208/ijnam2023-1009
UR - https://global-sci.org/intro/article_detail/ijnam/21354.html
KW - Parabolic equations, weak Galerkin method, non-smooth data, polygonal mesh, optimal $L^2$ error estimates.
AB - <p style="text-align: justify;">We analyze the weak Galerkin finite element methods for second-order linear
parabolic problems with $L^2$ initial data, both in a spatially semidiscrete case and in a fully
discrete case based on the backward Euler method. We have established optimal $L^2$ error
estimates of order $O(h^2/t)$ for semidiscrete scheme. Subsequently, the results are extended for fully discrete scheme. The error analysis has been carried out on polygonal meshes
for discontinuous piecewise polynomials in finite element partitions. Finally, numerical
experiments confirm our theoretical convergence results and efficiency of the scheme.</p>