Search results for "elliptic boundary value problems"

showing 3 items of 3 documents

Morse-Smale index theorems for elliptic boundary deformation problems.

2012

AbstractMorse-type index theorems for self-adjoint elliptic second order boundary value problems arise as the second variation of an energy functional corresponding to some variational problem. The celebrated Morse index theorem establishes a precise relation between the Morse index of a geodesic (as critical point of the geodesic action functional) and the number of conjugate points along the curve. Generalization of this theorem to linear elliptic boundary value problems appeared since seventies. (See, for instance, Smale (1965) [12], Uhlenbeck (1973) [15] and Simons (1968) [11] among others.) The aim of this paper is to prove a Morse–Smale index theorem for a second order self-adjoint el…

Pure mathematicsGeodesicApplied MathematicsMathematical analysisMixed boundary conditionSpectral flow Maslov index Index Theory Elliptic boundary value problemsElliptic boundary value problemsElliptic boundary value problemElliptic boundary deformation problemMaslov indexNeumann boundary conditionFree boundary problemSpectral flowElliptic boundary deformation problemsIndex TheoryBoundary value problemAtiyah–Singer index theoremAnalysisEnergy functionalMathematics
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Estimates of the modeling error generated by homogenization of an elliptic boundary value problem

2016

Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)

posteriori error estimateshomogenizationmodeling error010103 numerical & computational mathematics01 natural sciencesHomogenization (chemistry)Elliptic boundary value problem510 Mathematicselliptic boundary value problemsBoundary value problemNumerical testsperiodic structures0101 mathematicsMathematicsHomogenization510: Mathematik010102 general mathematicsMathematical analysisElliptic boundary value problemPeriodic structureModeling error10123 Institute of MathematicsComputational MathematicsExact solutions in general relativityRate of convergenceNorm (mathematics)A priori and a posteriori2605 Computational MathematicsA posteriori error estimateJournal of Numerical Mathematics
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Guaranteed error bounds for a class of Picard-Lindelöf iteration methods

2013

We present a new version of the Picard-Lindelof method for ordinary dif- ¨ ferential equations (ODEs) supplied with guaranteed and explicitly computable upper bounds of an approximation error. The upper bounds are based on the Ostrowski estimates and the Banach fixed point theorem for contractive operators. The estimates derived in the paper take into account interpolation and integration errors and, therefore, provide objective information on the accuracy of computed approximations. peerReviewed

Discrete mathematicsClass (set theory)Banach fixed-point theoremOdeguaranteed error boundsPicard-Lindelöf methodsinversio-ongelmatelliptic boundary value problemsPower iterationApproximation errorOrdinary differential equationComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONApplied mathematicsa posteriori estimatesObjective informationInterpolationMathematics
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