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In this paper, we will develop the convergence of the solution of TV-regularization equations with regularized parameter $\varepsilon \rightarrow 0$ in BV($\Omega$) for practical purposes. Originated from the effects of regularized parameter $\varepsilon$, the error rate of finite element approximation for TV-regularization equations will be controlled by the regularized parameter $\varepsilon^{-1}$ polynomially in the energy norm when using linearization technique and duality argument. And in the $L^p$-norm, the effect of regularized parameter $\varepsilon$ will be more extremely.
}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/824.html} }In this paper, we will develop the convergence of the solution of TV-regularization equations with regularized parameter $\varepsilon \rightarrow 0$ in BV($\Omega$) for practical purposes. Originated from the effects of regularized parameter $\varepsilon$, the error rate of finite element approximation for TV-regularization equations will be controlled by the regularized parameter $\varepsilon^{-1}$ polynomially in the energy norm when using linearization technique and duality argument. And in the $L^p$-norm, the effect of regularized parameter $\varepsilon$ will be more extremely.