Search results for "finite element approximation"

showing 5 items of 5 documents

Functional A Posteriori Error Estimates for Time-Periodic Parabolic Optimal Control Problems

2015

This article is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of the functional type, which are easily computable and provide guaranteed upper bounds for the state and co-state errors as well as for the cost functional. These theoretical results are confirmed by several numerical tests that show high efficiency of the a posteriori error bounds. peerReviewed

Mathematical optimizationControl and OptimizationMathematicsofComputing_NUMERICALANALYSISFinite element approximations010103 numerical & computational mathematicsType (model theory)01 natural sciencesparabolic time-periodic optimal control problemsError analysisFOS: MathematicsApplied mathematicsMathematics - Numerical AnalysisNumerical testsfunctional a posteriori error estimates0101 mathematicsMathematics - Optimization and Control49N20 35Q61 65M60 65F08Mathematicsta113Time periodicta111Numerical Analysis (math.NA)State (functional analysis)Optimal controlComputer Science Applications010101 applied mathematicsOptimization and Control (math.OC)multiharmonic finite element methodsSignal ProcessingA priori and a posterioriAnalysisNumerical Functional Analysis and Optimization
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A reliable incremental method of computing the limit load in deformation plasticity based on compliance : Continuous and discrete setting

2016

The aim of this paper is to introduce an enhanced incremental procedure that can be used for the numerical evaluation and reliable estimation of the limit load. A conventional incremental method of limit analysis is based on parametrization of the respective variational formulation by the loading parameter ? ? ( 0 , ? l i m ) , where ? l i m is generally unknown. The enhanced incremental procedure is operated in terms of an inverse mapping ? : α ? ? where the parameter α belongs to ( 0 , + ∞ ) and its physical meaning is work of applied forces at the equilibrium state. The function ? is continuous, nondecreasing and its values tend to ? l i m as α ? + ∞ . Reduction of the problem to a finit…

Pointwise convergenceReduction (recursion theory)Applied MathematicsMathematical analysista111Inverse010103 numerical & computational mathematics02 engineering and technologyFunction (mathematics)variational problems with linear growth energyfinite element approximation01 natural sciencesincremental limit analysisComputational Mathematics020303 mechanical engineering & transports0203 mechanical engineeringLimit analysisConvergence (routing)elastic-perfectly plastic problemsLimit loadLimit (mathematics)0101 mathematicsta216MathematicsJournal of Computational and Applied Mathematics
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Time Dependent Case

1999

This chapter is devoted to finite element approximations of scalar time dependent hemivariational inequalities. We start with the parabolic case following closely Miettinen and Haslinger, 1998. At the end of this chapter we discuss, how the results can be extended to constrained problems. Our presentation will follow the structure used for the static case in Chapter 3. First, we introduce an abstract formulation of a class of parabolic hemivariational inequalities (see Miettinen, 1996, Miettinen and Panagiotopoulos, 1999).

Scalar (mathematics)Applied mathematicsFinite element approximationsBilinear formFinite element methodMathematics
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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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On time-harmonic Maxwell equations with nonhomogeneous conductivities : Solvability and FE-approximation

1989

The solvability of time-harmonic Maxwell equations in the 3D-case with non­homogeneous conductivities is considered by adapting Sobolev space technique and variational formulation of the probJem in question. Moreover, a finite element approximation is presented in the 3D·case together with an error estimate in the energy norm. Some remarks are given to the 2D-problem arising from geophysics. peerReviewed

msc:35R05msc:65Z05msc:35Q20solution theory [keyword]msc:35Q99finite element approximation [keyword]msc:65N30time-harmonic Maxwell equations [keyword]non-homogeneous conductivities [keyword]error estimation [keyword]numerical experiments [keyword]msc:65N15three- dimensional problem [keyword]msc:78A25
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