Expanded mixed FEM with lowest order RT elements for nonlinear and nonlocal parabolic problems |
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Authors: | Nisha Sharma Amiya K. Pani Kapil K. Sharma |
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Affiliation: | 1.Department of Mathematics,MCM DAV College for Women,Chandigarh,India;2.Department of Mathematics, Industrial Mathematics Group,Indian Institute of Technology Bombay,Powai,India;3.Department of Mathematics,South Asian University,New Delhi,India |
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Abstract: | In this paper, an expanded mixed finite element method with lowest order Raviart Thomas elements is developed and analyzed for a class of nonlinear and nonlocal parabolic problems. After obtaining some regularity results for the exact solution, a priori error estimates for the semidiscrete problem are established. Based on a linearized backward Euler method, a complete discrete scheme is proposed and a variant of Brouwer’s fixed point theorem is used to derive an existence of a fully discrete solution. Further, a priori error estimates for the fully discrete scheme are established. Finally, numerical experiments are conducted to confirm our theoretical findings. |
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