35 research outputs found
Maximum norm a posteriori error estimation for parabolic problems using elliptic reconstructions
No full textA semilinear second-order parabolic equation is considered in a regular and a singularly perturbed regime. For this equation, we give computable a posteriori error estimates in the maximum norm. Semidiscrete and fully discrete versions of the backward Euler, Crank--Nicolson, and discontinuous Galerkin methods are addressed. For their full discretizations, we employ elliptic reconstructions that are, respectively, piecewise-constant, piecewise-linear, and piecewise-quadratic for in time. We also use certain bounds for the Green's function of the parabolic operator
Biomechanical analysis of temporomandibular joint dynamics based on real-time magnetic resonance imaging
No full textThe traditional hinge axis theory of temporomandibular joint (TMJ) dynamics is increasingly being replaced by the theory of instantaneous centers of rotation (ICR). Typically, ICR determinations are based on theoretical calculations or three-dimensional approximations of finite element models
Biomechanical analysis of temporomandibular joint dynamics based on real-time magnetic resonance imaging
No full textThe traditional hinge axis theory of temporomandibular joint (TMJ) dynamics is increasingly being replaced by the theory of instantaneous centers of rotation (ICR). Typically, ICR determinations are based on theoretical calculations or three-dimensional approximations of finite element models
Uniform pointwise convergence of finite difference schemes for quasilinear convection-diffusion problems
No full textCollocation methods for solving singular perturbation problems
No full textU disertaciji su razvijeni kolokacioni postupci sa C1- splajnovima proizvoljnog stepena za rešavanje singularno-perturbovanih problema reakcije-difuzije u jednoj i dve dimenzije. U 1D, pokazano je da kolokacioni postupak sa kvadratnim C1- splajnom na modifikovanoj Šiškinovoj mreži, konvergira uniformno, sa redom konvergencije skoro dva. Takođe, na gradiranim mrežama, ovaj metod ima red konvergencije dva – uniformno do na logaritamski faktor. Aposterirona ocena je postignuta za kolokacione postupke sa C1- splajnovima proizvoljnog stepena na proizvoljnoj mreži. Ova ocena je iskorišćena i za kreiranje adaptivnih mreža. Numerički rezultati povtrđuju dobijene ocene. U 2D su razmatrane kolokacije sa bikvadratnim splajnovima. Aposterirona ocena greške je postignuta. Numerički rezultati potvrđuju dobijene teorijske rezultate. Collocations with arbitrary order C1-splines for a singularly perturbed reaction-diffusion problem in one dimension and two dimensions are studied. In 1D, collocation with quadratic C1-splines is shown to be almost second order accurate on modified Shishkin mesh in the maximum norm, uniformly in the perturbation parameter. Also, we establish a second-order maximum norm a priori estimate on recursively graded mesh uniformly up to a logarithmic factor in the singular perturbation parameter. A posteriori error bounds are derived for the collocation method with arbitrary order C1-splines on arbitrary meshes. These bounds are used to drive an adaptivemeshmoving algorithm. An adaptive algorithm is devised to resolve the boundary layers. Numerical results are presented. In 2D, collocation with biquadratic C1-spline is studied. Robust a posteriori error bounds are derived for the collocation method on arbitrary meshes. Numerical experiments completed our theoretical results
Collocation methods for solving singular perturbation problems
No full textU disertaciji su razvijeni kolokacioni postupci sa C1- splajnovima proizvoljnog stepena za rešavanje singularno-perturbovanih problema reakcije-difuzije u jednoj i dve dimenzije. U 1D, pokazano je da kolokacioni postupak sa kvadratnim C1- splajnom na modifikovanoj Šiškinovoj mreži, konvergira uniformno, sa redom konvergencije skoro dva. Takođe, na gradiranim mrežama, ovaj metod ima red konvergencije dva – uniformno do na logaritamski faktor. Aposterirona ocena je postignuta za kolokacione postupke sa C1- splajnovima proizvoljnog stepena na proizvoljnoj mreži. Ova ocena je iskorišćena i za kreiranje adaptivnih mreža. Numerički rezultati povtrđuju dobijene ocene. U 2D su razmatrane kolokacije sa bikvadratnim splajnovima. Aposterirona ocena greške je postignuta. Numerički rezultati potvrđuju dobijene teorijske rezultate. Collocations with arbitrary order C1-splines for a singularly perturbed reaction-diffusion problem in one dimension and two dimensions are studied. In 1D, collocation with quadratic C1-splines is shown to be almost second order accurate on modified Shishkin mesh in the maximum norm, uniformly in the perturbation parameter. Also, we establish a second-order maximum norm a priori estimate on recursively graded mesh uniformly up to a logarithmic factor in the singular perturbation parameter. A posteriori error bounds are derived for the collocation method with arbitrary order C1-splines on arbitrary meshes. These bounds are used to drive an adaptivemeshmoving algorithm. An adaptive algorithm is devised to resolve the boundary layers. Numerical results are presented. In 2D, collocation with biquadratic C1-spline is studied. Robust a posteriori error bounds are derived for the collocation method on arbitrary meshes. Numerical experiments completed our theoretical results
A balanced finite-element method for an axisymmetrically loaded thin shell
No full textWe analyse a finite-element discretisation of a differential equation describing an axisymmetrically loaded thin shell. The problem is singularly perturbed when the thickness of the shell becomes small. We prove robust convergence of the method in a balanced norm that captures the layers present in the solution. Numerical results confirm our findings
Uniform convergence of a finite difference scheme for a system of coupledreaction‐diffusion equations
No full textA balanced finite-element method for an axisymmetrically loaded thin shell
No full textsummary:We analyse a finite-element discretisation of a differential equation describing an axisymmetrically loaded thin shell. The problem is singularly perturbed when the thickness of the shell becomes small. We prove robust convergence of the method in a balanced norm that captures the layers present in the solution. Numerical results confirm our findings
