Search results for "10123 Institute of Mathematics"

showing 4 items of 4 documents

A posteriori error majorants of the modeling errors for elliptic homogenization problems

2013

In this paper, we derive new two-sided a posteriori estimates of the modeling errors for linear elliptic boundary value problems with periodic coefficients solved by homogenization. Our approach is based on the concept of functional a posteriori error estimation. The estimates are obtained for the energy norm and use solely the global flux of the non-oscillatory solution of the homogenized model and solution of a boundary value problem on the cell of periodicity.

10123 Institute of Mathematics510 MathematicsNorm (mathematics)Mathematical analysista111A priori and a posterioriGeneral MedicineBoundary value problemHomogenization (chemistry)2600 General MathematicsMathematicsComptes Rendus Mathematique
researchProduct

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
researchProduct

Towards Stable Radial Basis Function Methods for Linear Advection Problems

2021

In this work, we investigate (energy) stability of global radial basis function (RBF) methods for linear advection problems. Classically, boundary conditions (BC) are enforced strongly in RBF methods. By now it is well-known that this can lead to stability problems, however. Here, we follow a different path and propose two novel RBF approaches which are based on a weak enforcement of BCs. By using the concept of flux reconstruction and simultaneous approximation terms (SATs), respectively, we are able to prove that both new RBF schemes are strongly (energy) stable. Numerical results in one and two spatial dimensions for both scalar equations and systems are presented, supporting our theoret…

Work (thermodynamics)AdvectionScalar (physics)Numerical Analysis (math.NA)35L65 41A05 41A30 65D05 65M12Stability (probability)Computational Mathematics10123 Institute of Mathematics510 MathematicsComputational Theory and MathematicsModeling and SimulationPath (graph theory)FOS: MathematicsApplied mathematicsRadial basis functionBoundary value problemMathematics - Numerical Analysis2605 Computational MathematicsEnergy (signal processing)Mathematics2611 Modeling and Simulation1703 Computational Theory and Mathematics
researchProduct

A posteriori modelling-discretization error estimate for elliptic problems with L ∞-Coefficients

2017

We consider elliptic problems with complicated, discontinuous diffusion tensor A0. One of the standard approaches to numerically treat such problems is to simplify the coefficient by some approximation, say Aϵ, and to use standard finite elements. In [19] a combined modelling-discretization strategy has been proposed which estimates the discretization and modelling errors by a posteriori estimates of functional type. This strategy allows to balance these two errors in a problem adapted way. However, the estimate of the modelling error was derived under the assumption that the difference A0 - Aϵ becomes small with respect to the L∞-norm. This implies in particular that interfaces/discontinui…

10123 Institute of Mathematics510 Mathematicselliptic regularity2604 Applied Mathematicsmodel simplification2612 Numerical Analysis2605 Computational Mathematicsa posteriori error estimation
researchProduct