Parabolic Problems

Granville Sewell
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Granville Sewell: University of Texas at El Paso, Mathematics Department

Chapter Chapter 4 in Analysis of a Finite Element Method, 1985, pp 77-93 from Springer

Abstract: Abstract The form of the time-dependent PDE system solved by PDE/PROTRAN (Section 1.5) is: (4.1.1) $$\begin{array}{*{20}{c}} {C(x,y,t,u){u_t}) = {A_x}(x,y,u,{u_x},{u_y}) + {B_y}(x,y,t,u,{u_x},{u_y}) + F(x,y,t,u,{u_x},{u_y})\,in\,R} \\ {u = FB(x,y,t)\,on\,\partial {R_1}} \\ {A{n_x} + B{n_y} = GB(x,y,t,u)\,on\,\partial {R_2}} \\ {u = UO(x,y)\,at\,t = {t_0}} \end{array}$$ where R is a general two dimesional region, $$\partial {R_1}\,and\,\partial {R_2}$$ are disjoint parts of the boundary, and C is a diagonal m by m matrix (m=number of PDEs).

Keywords: Finite Difference Method; Truncation Error; Time Step Size; Newton Iteration; Richardson Extrapolation (search for similar items in EconPapers)
Date: 1985
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DOI: 10.1007/978-1-4684-6331-6_4

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