A priori error estimates of expanded mixed FEM for Kirchhoff type parabolic equation
© 2019, Springer Science+Business Media, LLC, part of Springer Nature. For a nonlinear nonlocal parabolic problem containing the elastic energy coefficients, an expanded mixed finite element method using lowest order RT spaces is discussed in this paper. Firstly, some new regularity results are der...
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th-cmuir.6653943832-636892019-03-18T02:24:06Z A priori error estimates of expanded mixed FEM for Kirchhoff type parabolic equation Nisha Sharma Morrakot Khebchareon Amiya K. Pani Mathematics © 2019, Springer Science+Business Media, LLC, part of Springer Nature. For a nonlinear nonlocal parabolic problem containing the elastic energy coefficients, an expanded mixed finite element method using lowest order RT spaces is discussed in this paper. Firstly, some new regularity results are derived avoiding compatibility conditions on the data, which reflect behavior of exact solution as t → 0. Then, a semidiscrete method is derived on applying expanded mixed scheme in spatial direction keeping time variable continuous. A priori estimates for the discrete solutions are discussed under appropriate regularity assumptions and a priori error estimates in L ∞ (L 2 (Ω)) norm for the solution, the gradient and its flux are established for both the semidicsrete and fully discrete system, when the initial data is in H2(Ω)∩H01(Ω). Based on the backward Euler method, a completely discrete scheme is derived and existence of a unique fully discrete numerical solution is proved by using a variant of Brouwer’s fixed point theorem. Then, the corresponding error analysis is established. Further, numerical experiments are conducted for confirming our theoretical results. 2019-03-18T02:24:06Z 2019-03-18T02:24:06Z 2019-01-01 Journal 15729265 10171398 2-s2.0-85061273471 10.1007/s11075-019-00673-2 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85061273471&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/63689 |
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Mathematics Nisha Sharma Morrakot Khebchareon Amiya K. Pani A priori error estimates of expanded mixed FEM for Kirchhoff type parabolic equation |
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© 2019, Springer Science+Business Media, LLC, part of Springer Nature. For a nonlinear nonlocal parabolic problem containing the elastic energy coefficients, an expanded mixed finite element method using lowest order RT spaces is discussed in this paper. Firstly, some new regularity results are derived avoiding compatibility conditions on the data, which reflect behavior of exact solution as t → 0. Then, a semidiscrete method is derived on applying expanded mixed scheme in spatial direction keeping time variable continuous. A priori estimates for the discrete solutions are discussed under appropriate regularity assumptions and a priori error estimates in L ∞ (L 2 (Ω)) norm for the solution, the gradient and its flux are established for both the semidicsrete and fully discrete system, when the initial data is in H2(Ω)∩H01(Ω). Based on the backward Euler method, a completely discrete scheme is derived and existence of a unique fully discrete numerical solution is proved by using a variant of Brouwer’s fixed point theorem. Then, the corresponding error analysis is established. Further, numerical experiments are conducted for confirming our theoretical results. |
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Nisha Sharma Morrakot Khebchareon Amiya K. Pani |
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Nisha Sharma Morrakot Khebchareon Amiya K. Pani |
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Nisha Sharma |
title |
A priori error estimates of expanded mixed FEM for Kirchhoff type parabolic equation |
title_short |
A priori error estimates of expanded mixed FEM for Kirchhoff type parabolic equation |
title_full |
A priori error estimates of expanded mixed FEM for Kirchhoff type parabolic equation |
title_fullStr |
A priori error estimates of expanded mixed FEM for Kirchhoff type parabolic equation |
title_full_unstemmed |
A priori error estimates of expanded mixed FEM for Kirchhoff type parabolic equation |
title_sort |
priori error estimates of expanded mixed fem for kirchhoff type parabolic equation |
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2019 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85061273471&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/63689 |
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