Maximum norm contractivity of discretization schemes for the heat equation
Applied Numerical Mathematics
Maximum norm contractivity in the numerical solution of the one-dimensional heat equation
Applied Numerical Mathematics
Discrete Maximum Principle and Adequate Discretizations of Linear Parabolic Problems
SIAM Journal on Scientific Computing
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The preservation of the basic qualitative properties --- besides the convergence --- is a basic requirement in the numerical solution process. For solving the heat conduction equation, the finite difference/linear finite element Crank-Nicolson type full discretization process is a widely used approach. In this paper we formulate the discrete qualitative properties and we also analyze the condition w.r.t. the discretization step sizes under which the different qualitative properties are preserved. We give exact conditions for the discretization of the one-dimensional heat conduction problem under which the basic qualitative properties are preserved.