Search results for "error indicator"

showing 4 items of 4 documents

Fully reliable a posteriori error control for evolutionary problems

2015

Cauchy problemevolutionary problem of parabolic typeerror indicatorsosittaisdifferentiaaliyhtälötnumeeriset menetelmätvirheetOstrowski estimatesreaction-diffusion equationPoincaré-type estimatesnumeerinen analyysifunctional type a posteriori error estimatesepäyhtälötvirheanalyysiPicard-Lindelöf methoddifferentiaaliyhtälöt
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Reliable numerical solution of a class of nonlinear elliptic problems generated by the Poisson-Boltzmann equation

2020

We consider a class of nonlinear elliptic problems associated with models in biophysics, which are described by the Poisson-Boltzmann equation (PBE). We prove mathematical correctness of the problem, study a suitable class of approximations, and deduce guaranteed and fully computable bounds of approximation errors. The latter goal is achieved by means of the approach suggested in [S. Repin, A posteriori error estimation for variational problems with uniformly convex functionals. Math. Comp., 69:481-500, 2000] for convex variational problems. Moreover, we establish the error identity, which defines the error measure natural for the considered class of problems and show that it yields computa…

a priori error estimatesClass (set theory)Correctness010103 numerical & computational mathematics01 natural sciencesMeasure (mathematics)guaranteed and efficient a posteriori error boundsFOS: MathematicsApplied mathematicsPolygon meshMathematics - Numerical Analysis0101 mathematicserror indicators and adaptive mesh refinementMathematicsNumerical AnalysisApplied MathematicsRegular polygonNumerical Analysis (math.NA)convergence of finite element approximationsLipschitz continuity010101 applied mathematicsComputational MathematicsNonlinear systemexistence and uniqueness of solutionssemilinear partial differential equations65J15 49M29 65N15 65N30 65N50 35J20MathematikA priori and a posterioriPoisson-Boltzmann equationdifferentiaaliyhtälöt
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New Indicators of Approximation Errors for Problems in Continuum Mechanics

2010

In this paper we present a new error indicator for approximate solutions of elliptic problems. We discuss error indication with the paradigm of the diffusion problem, however the techniques are easily adaptable to more complicated elliptic problems, for example to linear elasticity, viscous flow models and electromagnetic models. The proposed indicator does not contain mesh dependent constants and it admits parallelization. nonPeerReviewed

continuum mechanicskokemuksellisuuserror indicatorreliable numerical methods
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A posteriori error control for Maxwell and elliptic type problems

2014

osittaisdifferentiaaliyhtälöterror equalitynumeeriset menetelmätfunctional a posteriori error controlsähkömagneettiset kentäterror indicatorvirheeterror estimatenumeerinen analyysiMaxwell type problemvirheanalyysielliptic problemeddy-current problem
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