Convergence of
H
1-Galerkin mixed finite element method for parabolic problems with reduced regularity of initial datas
M. Tripathy, Rajen Kumar Sinha
Indian Institute of Technology Guwahati, Guwahati, 781039, India
Keywords: параболические задачи, H
-смешанный метод конечных элементов Галеркина, полудискретная схема, обратный метод Эйлера, оценки ошибки, parabolic problems, H
-Galerkin mixed finite element method, semi-discrete scheme, backward Euler method, error estimates
Abstract
We study the convergence of an
H
1-Galerkin mixed finite element method for parabolic problems in one space dimension. Both semi-discrete and fully discrete schemes are analyzed assuming reduced regularity of the initial data. More precisely, for a spatially discrete scheme error estimates of order \mathcal{O}(
h
2
t
-1/2) for positive time are established assuming the initial function
p
0 ϶
H
2(Ω) ∩
H
0
1(Ω). Further, we use an energy technique together with a parabolic duality argument to derive error estimates of order \mathcal{O}(
h
2
t
-1) when
p
0 is only in
H
0
1(Ω). A discrete-in-time backward Euler method is analyzed and almost optimal order error bounds are established.
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