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Finite element analysis and approximation of Burgers’‐Fisher equation
Author(s) -
Yadav Om Prakash,
Jiwari Ram
Publication year - 2017
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22158
Subject(s) - mathematics , discretization , backward euler method , finite element method , burgers' equation , partial differential equation , uniqueness , norm (philosophy) , nonlinear system , convergence (economics) , mixed finite element method , mathematical analysis , discontinuous galerkin method , a priori and a posteriori , philosophy , physics , epistemology , quantum mechanics , political science , law , economics , thermodynamics , economic growth
In this article, the authors present finite element analysis and approximation of Burgers’‐Fisher equation. Existence and uniqueness of weak solution is proved by Galerkin's finite element method for non‐smooth initial data. Next, a priori error estimates of semi‐discrete solution inL ∞ ( 0 , T ; L 2 ( Ω ) ) norm, are derived and the convergence of semi‐discrete solution is established. Then, fully discretization of the problem is done with the help of Euler's backward method. The nonlinearity is removed by lagging it to previous known level. The scheme is found to be convergent. Positivity of fully discrete solution is discussed, and bounds on time step are discovered for which the solution preserves its positivity. Finally, numerical experiments are performed on some examples to demonstrate the effectiveness of the scheme. The proposed scheme found to be fast, easy and accurate.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1652–1677, 2017