Search results for " boundary value problem"

showing 4 items of 54 documents

On FE-grid relocation in solving unilateral boundary value problems by FEM

1992

We consider FE-grid optimization in elliptic unilateral boundary value problems. The criterion used in grid optimization is the total potential energy of the system. It is shown that minimization of this cost functional means a decrease of the discretization error or a better approximation of the unilateral boundary conditions, Design sensitivity analysis is given with respect to the movement of nodal points. Numerical results for the Dirichlet-Signorini problem for the Laplace equation and the plane elasticity problem with unilateral boundary conditions are given. In plane elasticity we consider problems with and without friction. peerReviewed

finite element methods [keyword]msc:65N50numerical examples [keyword]FE-grid relocation [keyword]msc:65N30nonlinear optimization [keyword]msc:35J05sequential quadratic programming code [keyword]unilateral boundary value problem [keyword]Poisson equation [keyword]grid relocation [keyword]
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Optimality of Increasing Stability for an Inverse Boundary Value Problem

2021

In this work we study the optimality of increasing stability of the inverse boundary value problem (IBVP) for the Schrödinger equation. The rigorous justification of increasing stability for the IBVP for the Schrödinger equation were established by Isakov [Discrete Contin. Dyn. Syst. Ser. S, 4 (2011), pp. 631--640] and by Isakov et al. [Inverse Problems and Applications, Contemp. Math. 615, American Math Society, Providence, RI, 2014, pp. 131--141]. In [Discrete Contin. Dyn. Syst. Ser. S, 4 (2011), pp. 631--640] and [Inverse Problems and Applications, Contemp. Math. 615, American Math Society, Providence, RI, 2014, pp. 131--141], the authors showed that the stability of this IBVP increases …

increasing stability phenomenaosittaisdifferentiaaliyhtälötinstabilityComputational MathematicsMathematics - Analysis of PDEsApplied Mathematics35J15 35R25 35R30FOS: MathematicsSchrödinger equationinverse boundary value probleminversio-ongelmatAnalysisAnalysis of PDEs (math.AP)SIAM Journal on Mathematical Analysis
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Multiplicity results for asymmetric boundary value problems with indefinite weights

2004

We prove existence and multiplicity of solutions, with prescribed nodal properties, to a boundary value problem of the formu″+f(t,u)=0,u(0)=u(T)=0. The nonlinearity is supposed to satisfy asymmetric, asymptotically linear assumptions involving indefinite weights. We first study some auxiliary half-linear, two-weighted problems for which an eigenvalue theory holds. Multiplicity is ensured by assumptions expressed in terms of weighted eigenvalues. The proof is developed in the framework of topological methods and is based on some relations between rotation numbers and weighted eigenvalues.

lcsh:MathematicsApplied MathematicsMultiplicity resultsMathematical analysis34B15Of the formMultiplicity (mathematics)Mixed boundary conditionlcsh:QA1-939Asymmetric boundary value problem asymptotically linear two-weighted problems eigenvalue theory topological methods rotation number multiplicity resultFree boundary problemBoundary value problemAnalysisMathematicsAbstract and Applied Analysis
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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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