Regularity analyses and approximation of nonlocal variational equality and inequality problems
| Autor: | Olena Burkovska, Max D. Gunzburger |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Inequality
Anomalous diffusion Applied Mathematics media_common.quotation_subject 010102 general mathematics 01 natural sciences 010101 applied mathematics symbols.namesake Operator (computer programming) TheoryofComputation_LOGICSANDMEANINGSOFPROGRAMS Lagrange multiplier Bounded function symbols Applied mathematics Ball (mathematics) 0101 mathematics Laplace operator Vector calculus Analysis Mathematics media_common |
| Zdroj: | Journal of Mathematical Analysis and Applications. 478:1027-1048 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2019.05.064 |
| Popis: | We consider linear and obstacle problems driven by a nonlocal integral operator, for which nonlocal interactions are restricted to a ball of finite radius. These types of operators are used to model anomalous diffusion and, for a special choice of the integral kernels, reduce to the fractional Laplace operator on a bounded domain. By means of a nonlocal vector calculus we recast the problems in a weak form, leading to corresponding nonlocal variational equality and inequality problems. We prove optimal regularity results for both problems, including a higher regularity of the solution and the Lagrange multiplier. Based on the regularity results, we analyze the convergence of finite element approximations for a linear problem and illustrate the theoretical findings by numerical results. |
| Databáze: | OpenAIRE |
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