A priori error bounds for parabolic interface problems with measure data
Gupta Jhuma Sen
Department of Mathematics, Bits Pilani Hyderabad, Hyderabad, India
Keywords: parabolic interface problems, spatially discrete and fully discrete finite element approximation, a priori error analysis, measure data
Abstract
This article studies a priori error analysis for linear parabolic interface problems with measure data in time in a bounded convex polygonal domain in R2. Both the spatially discrete and the fully discrete approximations are analyzed. We have used the standard continuous fitted finite element discretization for the space while, the backward Euler approximation is used for the time discretization. Due to the low regularity of the data of the problem, the solution possesses very low regularity in the entire domain. A priori error bounds in the L2(L2(Ω))-norm for both the spatially discrete and the fully discrete finite element approximations are derived under minimal regularity with the help of the L2-projection operator and the duality argument. Numerical experiments are performed to underline the theoretical findings. The interfaces are assumed to be smooth for our purpose.
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