Sökning: "Multiscale Elliptic Equation"

Hittade 5 avhandlingar innehållade orden Multiscale Elliptic Equation.

  1. 1. Analysis and Applications of the Heterogeneous Multiscale Methods for Multiscale Elliptic and Hyperbolic Partial Differential Equations

    Författare :Doghonay Arjmand; Olof Runborg; Axel Målqvist; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Multiscale Methods; HMM; Multiscale Wave Equation; Multiscale Elliptic Equation; Long Time Wave Propagation; SRA - E-vetenskap SeRC ; SRA - E-Science SeRC ;

    Sammanfattning : This thesis concerns the applications and analysis of the Heterogeneous Multiscale methods (HMM) for Multiscale Elliptic and Hyperbolic Partial Differential Equations. We have gathered the main contributions in two papers. LÄS MER

  3. 2. Adaptive variational multiscale methods

    Författare :Axel Målqvist; Göteborgs universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; finite element method; Galerkin; duality; a posteriori error estimation; adaptivity; variational multiscale method; mixed formulation; multi-physics; oil reservoir simulation; finite element method;

    Sammanfattning : In this thesis we present a new adaptive multiscale method for solving elliptic partial differential equations. The method is based on numerical solution of decoupled local fine scale problems on patches. LÄS MER

  4. 3. Mathematical analysis and approximation of a multiscale elliptic-parabolic system

    Författare :Omar Richardson; Adrian Muntean; Alfred Schmidt; Karlstads universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Two-scale modelling; two-scale Galerkin approximation; inverse Robin estimates; elliptic-parabolic system; a priori analysis; a posteriori error estimators; Matematik; Mathematics;

    Sammanfattning : We study a two-scale coupled system consisting of a macroscopic elliptic equation and a microscopic parabolic equation. This system models the interplay between a gas and liquid close to equilibrium within a porous medium with distributed microstructures. We use formal homogenization arguments to derive the target system. LÄS MER

  5. 4. Analysis and Applications of Heterogeneous Multiscale Methods for Multiscale Partial Differential Equations

    Författare :Doghonay Arjmand; Olof Runborg; Marcus Grote; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Numerical homogenization; long time wave propagation; multiscale PDEs; Tillämpad matematik och beräkningsmatematik; Applied and Computational Mathematics;

    Sammanfattning : This thesis centers on the development and analysis of numerical multiscale methods for multiscale problems arising in steady heat conduction, heat transfer and wave propagation in heterogeneous media. In a multiscale problem several scales interact with each other to form a system which has variations over a wide range of scales. LÄS MER

  7. 5. Two Problems in non-linear PDE’s with Phase Transitions

    Författare :Karl Jonsson; Henrik Shahgholian; Tomas Sjödin; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Conductivity jump; Free boundary problem; Quasilinear elliptic equation; Mathematical techniques; Nonlinear analysis; Free boundary; Free-boundary problems; Quasi-linear elliptic; Quasilinear elliptic equations; Hele-Shaw flow; non-local; implicit function theorem; Heterogeneous Multi Scale; HMM; Finite Element; FEM; FE; Mathematics; Matematik;

    Sammanfattning : This thesis is in the field of non-linear partial differential equations (PDE), focusing on problems which show some type of phase-transition. A single phase Hele-Shaw flow models a Newtoninan fluid which is being injected in the space between two narrowly separated parallel planes. LÄS MER