A comparison of the String Gradient Weighted Moving Finite Element method and a Parabolic Moving Mesh Partial Differential Equation method for solutions of partial differential equations
We compare numerical experiments from the String Gradient Weighted Moving Finite Element method and a Parabolic Moving Mesh Partial Differential Equation method, applied to three benchmark problems based on two different partial differential equations. Both methods are described in detail and we highlight some strengths and weaknesses of each method via the numerical comparisons. The two equations used in the benchmark problems are the viscous Burgers' equation and the porous medium equation, both in one dimension. Simulations are made for the two methods for: a) a travelling wave solution for the viscous Burgers' equation, b) the Barenblatt selfsimilar analytical solution of the porous medium equation, and c) a waiting-time solution for the porous medium equation. Simulations are carried out for varying mesh sizes, and the numerical solutions are compared by computing errors in two ways. In the case of an analytic solution being available, the errors in the numerical solutions are computed directly from the analytic solution. In the case of no availability of an analytic solution, an approximation to the error is computed using a very fine mesh numerical solution as the reference solution.
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España
Mostrando ítems relacionados por Título, autor o materia.
Pagnini, G. (2017-06-20)It is well known that the Michelson-Sivashinky equation describes hydrodynamic instabilities in turbulent premixed combustion. Here a formulation of the flame front propagation based on the G-equation and on stochastic ...
On the regularity of null-controls of the linear 1-d heat equation [Sur la regularité des contrôles pour l'équation de la chaleur linéaire] Micu, S.; Zuazua, E. (2011-12-31)The 1-d heat equation in a bounded interval is null-controllable from the boundary. More precisely, for each initial data y0εL2(0,1) there corresponds a unique boundary control of minimal L2(0,T)-norm which drives the state ...
Ignat, L.I.; Pazoto, A.F.; Rosier, L. (2012-12-31)In this paper, we establish global Carleman estimates for the heat and Schrödinger equations on a network. The heat equation is considered on a general tree and the Schrödinger equation on a star-shaped tree. The Carleman ...