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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.13694 |
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| _version_ | 1866918510489239552 |
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| author | Leykekhman, Dmitriy Vexler, Boris Wagner, Jakob |
| author_facet | Leykekhman, Dmitriy Vexler, Boris Wagner, Jakob |
| contents | In this paper we analyze a homogeneous parabolic problem with initial data in the space of regular Borel measures. The problem is discretized in time with a discontinuous Galerkin scheme of arbitrary degree and in space with continuous finite elements of orders one or two. We show parabolic smoothing results for the continuous, semidiscrete and fully discrete problems. Our main results are interior $L^\infty$ error estimates for the evaluation at the endtime, in cases where the initial data is supported in a subdomain. In order to obtain these, we additionally show interior $L^\infty$ error estimates for $L^2$ initial data and quadratic finite elements, which extends the corresponding result previously established by the authors for linear finite elements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_13694 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fully Discrete Pointwise Smoothing Error Estimates for Measure Valued Initial Data Leykekhman, Dmitriy Vexler, Boris Wagner, Jakob Numerical Analysis 65N30, 65N15 In this paper we analyze a homogeneous parabolic problem with initial data in the space of regular Borel measures. The problem is discretized in time with a discontinuous Galerkin scheme of arbitrary degree and in space with continuous finite elements of orders one or two. We show parabolic smoothing results for the continuous, semidiscrete and fully discrete problems. Our main results are interior $L^\infty$ error estimates for the evaluation at the endtime, in cases where the initial data is supported in a subdomain. In order to obtain these, we additionally show interior $L^\infty$ error estimates for $L^2$ initial data and quadratic finite elements, which extends the corresponding result previously established by the authors for linear finite elements. |
| title | Fully Discrete Pointwise Smoothing Error Estimates for Measure Valued Initial Data |
| topic | Numerical Analysis 65N30, 65N15 |
| url | https://arxiv.org/abs/2304.13694 |