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- W2322064322 abstract "AbstractTypically when a semi-discrete approximation to a partial differential equation (PDE) is constructed a discretization of the spatial operator with a truncation error τ is derived. This discrete operator should be semi-bounded for the scheme to be stable. Under these conditions the Lax–Richtmyer equivalence theorem assures that the scheme converges and that the error will be, at most, of the order of (|tau |). In most cases the error is in indeed of the order of (|tau |). We demonstrate that for the Heat equation stable schemes can be constructed, whose truncation errors are τ, however, the actual errors are much smaller. This gives more degrees of freedom in the design of schemes which can make them more efficient (more accurate or compact) than standard schemes. In some cases the accuracy of the schemes can be further enhanced using post-processing procedures.KeywordsHeat EquationTruncation ErrorDiscontinuous Galerkin MethodOrder SchemeHigh Frequency ModeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
- W2322064322 created "2016-06-24" @default.
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- W2322064322 date "2015-01-01" @default.
- W2322064322 modified "2023-09-24" @default.
- W2322064322 title "High Order Finite Difference Schemes for the Heat Equation Whose Convergence Rates are Higher Than Their Truncation Errors" @default.
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- W2322064322 doi "https://doi.org/10.1007/978-3-319-19800-2_13" @default.
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