# Numerical Methods for Partial Differential Equations

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^{1}‐Galerkin mixed finite element method for a nonlinear parabolic equation, which models a compressible fluid flow process in subsurface porous media. The method possesses the advantages of mixed finite element methods while avoiding directly inverting the permeability tensor, which is important especially in a low permeability zone. We conducted theoretical analysis to study the existence...

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*Appl Math Comput*201(2008), 229–238). In Sharma and Singh, the authors consider the problem with sufficiently small shift arguments. The term negative shift and positive shift are used for delay and advance arguments, respectively. Here, we propose a numerical...

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*N*‐carrier system with heat sources and Neumann boundary conditions, which extends the concept of the well‐known parabolic two‐step model for microheat transfer. By using the matrix analysis, the compact finite difference numerical scheme is shown to be unconditionally...

Numerical Methods for Partial Differential Equations > 26 > 2 > 480 - 489