Found 186 Documents (Results 1–100)
A second-order in time, BGN-based parametric finite element method for geometric flows of curves. (English) Zbl 07898991
An operator-splitting optimization approach for phase-field simulation of equilibrium shapes of crystals. (English) Zbl 07860849
A structure-preserving parametric finite element method for geometric flows with anisotropic surface energy. (English) Zbl 1541.65089
Numerical surgery for mean curvature flow of surfaces. (English) Zbl 1540.65379
Reviewer: Shuji Yoshikawa (Ōita)
New artificial tangential motions for parametric finite element approximation of surface evolution. (English) Zbl 1536.53177
Reviewer: Xiaodi Zhang (Zhengzhou)
Parametric finite element approximations for anisotropic surface diffusion with axisymmetric geometry. (English) Zbl 07811320
A numerical domain decomposition method for solving elliptic equations on manifolds. (English) Zbl 1532.65105
Fractional elliptic problems on Lipschitz domains: regularity and approximation. (English) Zbl 1532.65104
Mengesha, Tadele (ed.) et al., A\(^3\)N\(^2\)M: approximation, applications, and analysis of nonlocal, nonlinear models. Proceedings of the 50th John H. Barrett memorial lectures, Knoxville, TN, USA, virtual, May 2021. Cham: Springer. IMA Vol. Math. Appl. 165, 27-99 (2023).
A structure-preserving finite element approximation of surface diffusion for curve networks and surface clusters. (English) Zbl 1531.65156
Numerical analysis for a system coupling curve evolution attached orthogonally to a fixed boundary, to a reaction-diffusion equation on the curve. (English) Zbl 1533.65184
A convergent finite element algorithm for mean curvature flow in arbitrary codimension. (English) Zbl 07761250
A symmetrized parametric finite element method for simulating solid-state dewetting problems. (English) Zbl 1525.65124
MSC:
65N30
A convexity-preserving and perimeter-decreasing parametric finite element method for the area-preserving curve shortening flow. (English) Zbl 1522.65174
Stabilized finite element approximation of the Swift-Hohenberg model on evolving surfaces. (English) Zbl 07733013
Global polynomial level sets for numerical differential geometry of smooth closed surfaces. (English) Zbl 1527.53092
Reviewer: Krzysztof Gdawiec (Sosnowiec)
A structure preserving front tracking finite element method for the Mullins-Sekerka problem. (English) Zbl 07711459
Reviewer: Bülent Karasözen (Ankara)
A symmetrized parametric finite element method for anisotropic surface diffusion in three dimensions. (English) Zbl 1518.65106
Structure-preserving discretizations of two-phase Navier-Stokes flow using fitted and unfitted approaches. (English) Zbl 07705917
Second-order accurate finite volume method for \(G\)-equation on polyhedral meshes. (English) Zbl 1518.65099
Reviewer: Abdallah Bradji (Annaba)
“Gradient-free” diffuse approximations of the Willmore functional and Willmore flow. (English) Zbl 1530.35212
A structure-preserving parametric finite element method for area-conserved generalized curvature flow. (English) Zbl 1516.65096
A symmetrized parametric finite element method for anisotropic surface diffusion of closed curves. (English) Zbl 1512.65205
Reviewer: Marius Ghergu (Dublin)
Equivalence between a time-fractional and an integer-order gradient flow: the memory effect reflected in the energy. (English) Zbl 1500.35294
Computing confined elasticae. (English) Zbl 1535.74639
Optimal control of a quasilinear parabolic equation and its time discretization. (English) Zbl 1497.35305
Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces. (English) Zbl 07565226
Volume-preserving parametric finite element methods for axisymmetric geometric evolution equations. (English) Zbl 07525159
Poincaré inequality for a mesh-dependent 2-norm on piecewise linear surfaces with boundary. (English) Zbl 1482.65216
A novel \(W^{1,\infty}\) approach to shape optimisation with Lipschitz domains. (English) Zbl 1483.35299
A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations. (English) Zbl 1507.92009
A priori error estimates for finite element approximations of regularized level set flows in higher norms. (English) Zbl 1525.65122
High-order fully discrete energy diminishing evolving surface finite element methods for a class of geometric curvature flows. (English) Zbl 1499.65491
A perimeter-decreasing and area-conserving algorithm for surface diffusion flow of curves. (English) Zbl 07515430
A Convergent evolving finite element algorithm for Willmore flow of closed surfaces. (English) Zbl 1496.65165
Numerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifolds. (English) Zbl 1478.65084
A class of second-order geometric quasilinear hyperbolic PDEs and their application in imaging. (English) Zbl 1478.35150
Error analysis for a finite difference scheme for axisymmetric mean curvature flow of genus-0 surfaces. (English) Zbl 1479.65003
An adaptive threshold dynamics method for three-dimensional wetting on rough surfaces. (English) Zbl 1473.65149
Computational treatment of interface dynamics via phase-field modeling. (English) Zbl 1481.76263
Greiner, David (ed.) et al., Numerical simulation in physics and engineering: trends and applications. Lecture notes of the XVIII ‘Jacques-Louis Lions’ Spanish-French school, Las Palmas de Gran Canaria, Spain, June 25–29, 2018. Cham: Springer. SEMA SIMAI Springer Ser. 24, 81-118 (2021).
Convergence of Dziuk’s semidiscrete finite element method for mean curvature flow of closed surfaces with high-order finite elements. (English) Zbl 1479.65008
SIAM J. Numer. Anal. 59, No. 3, 1592-1617 (2021); erratum ibid. 61, No. 3, 1609-1612 (2023).
Reviewer: J. Manimaran (Ponda)
On the sharp interface limit of a model for phase separation on biological membranes. (English) Zbl 1465.35024
Dynamics of curved travelling fronts for the discrete Allen-Cahn equation on a two-dimensional lattice. (English) Zbl 1481.34018
Reviewer: Caidi Zhao (Wenzhou)
Numerical methods for biomembranes: conforming subdivision methods versus non-conforming PL methods. (English) Zbl 1455.49023
Fitted front tracking methods for two-phase ncompressible Navier-Stokes flow: Eulerian and ALE finite element discretizations. (English) Zbl 1471.76084
Linear and nonlinear fractional elliptic problems. (English) Zbl 1481.65220
Brenner, Susanne C. (ed.) et al., 75 years of mathematics of computation. Symposium celebrating 75 years of mathematics of computation, Institute for Computational and Experimental Research in Mathematics, ICERM, Providence, RI, USA, November 1–3, 2018. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 754, 69-92 (2020).
Structure preserving discretization of Allen-Cahn type problems modeling the motion of phase boundaries. (English) Zbl 1471.65134
Reviewer: Marius Ghergu (Dublin)
A convergent algorithm for forced mean curvature flow driven by diffusion on the surface. (English) Zbl 1458.35016
A second-order stabilization method for linearizing and decoupling nonlinear parabolic systems. (English) Zbl 1453.65226
Reviewer: Qifeng Zhang (Hangzhou)
A domain mapping approach for elliptic equations posed on random bulk and surface domains. (English) Zbl 1452.65330
Sharp-interface model for simulating solid-state dewetting in three dimensions. (English) Zbl 1440.74153
A stable finite element method for low inertia undulatory locomotion in three dimensions. (English) Zbl 1443.74266
A parametric finite element method for solid-state dewetting problems in three dimensions. (English) Zbl 1430.74056
Numerical modeling of non-isothermal compositional compressible gas flow in soil and coupled atmospheric boundary layer. (English) Zbl 1484.76044
Sharp-interface approach for simulating solid-state dewetting in two dimensions: A Cahn-hoffman \(\boldsymbol{\xi}\)-vector formulation. (English) Zbl 1448.74097
Isogeometric analysis for phase-field models of geometric PDEs and high-order PDEs on stationary and evolving surfaces. (English) Zbl 1441.65023
The dynamics of geometric PDEs: surface evolution equations and a comparison with their small gradient approximations. (English) Zbl 1430.53106
A convergent evolving finite element algorithm for mean curvature flow of closed surfaces. (English) Zbl 1427.65250
Analysis of constants in error estimates for the finite element approximation of regularized nonlinear geometric evolution equations. (English) Zbl 1451.65198
Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca)
Discrete gradient flows for General curvature energies. (English) Zbl 1434.65178
Reviewer: Song Jiang (Beijing)
Finite element methods for fourth order axisymmetric geometric evolution equations. (English) Zbl 1416.65334
Variational discretization of axisymmetric curvature flows. (English) Zbl 1419.65051
Reviewer: Dana Černá (Liberec)
A high-order FEM with exact geometry description for the Laplacian on implicitly defined surfaces. (English) Zbl 07878355
Analysis and numerical solution of coupled volume-surface reaction-diffusion systems with application to cell biology. (English) Zbl 1427.65243
Gradient flow dynamics of two-phase biomembranes: sharp interface variational formulation and finite element approximation. (English) Zbl 1416.74070
Evolving surface finite element methods for random advection-diffusion equations. (English) Zbl 1407.65258
Finite element approximation of level set motion by powers of the mean curvature. (English) Zbl 1404.35215
Multiphase mean curvature flows with high mobility contrasts: a phase-field approach, with applications to nanowires. (English) Zbl 1395.65097
Domain-growth-induced patterning for reaction-diffusion systems with linear cross-diffusion. (English) Zbl 1394.35242
Unconditional stability of semi-implicit discretizations of singular flows. (English) Zbl 1394.65098
Reviewer: Piotr Biler (Wrocław)
A finite area scheme for shallow granular flows on three-dimensional surfaces. (English) Zbl 1390.76904
MSC:
76T25
76M25
Application of the moving frame method to deformed Willmore surfaces in space forms. (English) Zbl 1388.53054
An efficient boundary integral scheme for the MBO threshold dynamics method via the NUFFT. (English) Zbl 1419.65080
Projected finite elements for systems of reaction-diffusion equations on closed evolving spheroidal surfaces. (English) Zbl 1488.65460
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