Maximum-Norm Stability and Error Estimates
The main purpose in this chapter is to discuss stability estimates for the semidiscrete solution of the homogeneous heat equation in the maximumnorm, and their consequences for error bounds for problems with smooth and nonsmooth initial data. The proofs of the stability estimates are considerably more complicated than for those in the L 2-norm of our earlier chapters, and will be carried out by a weighted norm technique. For the error estimates we need to do some auxiliary work in L p with p large.
KeywordsSolution Operator Logarithmic Factor Resolvent Estimate Smoothing Estimate Piecewise Linear Finite Element
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