Analysis of the Fictitious Domain Method with H-penalty for Parabolic Problem
نویسندگان
چکیده
We consider the fictitious domain method with H1-penalty for a parabolic problem. First, the sharp error estimate for the H1penalty problem approximating the original problem is derived. Then, we present some regularity analysis and prior estimate to the H1-penalty problem. The finite element approximation is investigated for discrete problems of two types, “continuous-time” and “single-step backward”. To perform the numerical computation, we provide an approximation scheme for the “single-step backward” discrete problem as well as its error estimate. The theoretical result is verified using our numerical experiment.
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