Abstract:ABSTRACT. In this work we present an efficient Galerkin least squares finite element scheme to simulate the Burgers' equation on the whole real line and subjected to initial conditions with compact support. The numerical simulations are performed by considering a sequence of auxiliary spatially dimensionless Dirichlet's problems parameterized by its numerical supportK . Gaining advantage from the well-known convective-diffusive effects of the Burgers' equation, computations start by choosingK so it contains th… Show more
“…Besides that, according to [5] whose article presents a finite element schema of second order precision to simulate a Burgers equation, as direct comparisons between analytical and numerical solutions show that the proposed scheme has good precision. In addition, the asymptotic behaviour of indicative analysis solutions such as simulations maintains good accuracy over very large time intervals.…”
This paper aims to apply the High Order Explicit Finite Difference Method to solve the famous Nonlinear 1D Burgers Equation in many orders in time (first, second, third and fourth), changing the order on space twice (second and fourth). Thereby, it was compared the results and it was found the best refinement. Thus, it is expected that this work not only can present or even confirm that in most cases greater refinements imply better numerical precision, but rather serve as a basis for decision-making when analyzing the best spatial and should be considered for numerical accuracy and low computational time.
“…Besides that, according to [5] whose article presents a finite element schema of second order precision to simulate a Burgers equation, as direct comparisons between analytical and numerical solutions show that the proposed scheme has good precision. In addition, the asymptotic behaviour of indicative analysis solutions such as simulations maintains good accuracy over very large time intervals.…”
This paper aims to apply the High Order Explicit Finite Difference Method to solve the famous Nonlinear 1D Burgers Equation in many orders in time (first, second, third and fourth), changing the order on space twice (second and fourth). Thereby, it was compared the results and it was found the best refinement. Thus, it is expected that this work not only can present or even confirm that in most cases greater refinements imply better numerical precision, but rather serve as a basis for decision-making when analyzing the best spatial and should be considered for numerical accuracy and low computational time.
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