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ProblemsClear skill: Weak Galerkin Build a practice set

ProblemCourse & topicStatus

FEM:9911001Consider the boundary-value problem -u''(x)=x for 0<x<1, with u(0)=u(1)=0.

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911002Mathematical problem title

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911003Consider -u''(x)=1+x for 0<x<1, with u(0)=u(1)=0.

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911004Mathematical problem title

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911005Consider -u''(x)+2u(x)=1 on 0<x<1, with nonhomogeneous boundary conditions u(0)=1 and u(1)=0.

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911006For the mixed-boundary problem -u''(x)+u(x)=x on 0<x<1, with u(0)=0 and u'(1)=1, use the Galerkin approximation…

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911007Mathematical problem title

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911008Mathematical problem title

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911009Mathematical problem title

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911010Solve -u''(x)=1 on 0<x<1, with u(0)=u(1)=0, by the continuous piecewise-linear Galerkin finite element method on…

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911011Let u(x) denote the axial displacement of a uniform elastic bar occupying 0<x<2.

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911012Mathematical problem title

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911013Mathematical problem title

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911014Solve -u''(x)=x on 0<x<1 with the inhomogeneous essential conditions u(0)=2 and u(1)=-1 by a Galerkin finite…

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911015An elastic bar of length 4 has constant axial rigidity EA=12 and is discretized by two linear elements with nodes…

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911016Mathematical problem title

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911017Mathematical problem title

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911018Mathematical problem title

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911019Mathematical problem title

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911020Mathematical problem title

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911021A straight axial bar is modeled by three two-node linear bar elements connecting nodes at x = 0, 0.40, 1.00, and…

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911022Three collinear nodes have scalar horizontal displacements u1, u2, and u3.

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911023A uniform axial bar of length 2.0 m and constant rigidity EA = 80 MN is fixed at x = 0 and represented by two…

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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FEM:9911024A tapered axial member occupies 0 <= x <= 1.2 m, has Young's modulus E = 70 GPa, and has cross-sectional area A(x)…

Weak GalerkinFinite Element Methods Problem Solving

Weak formulations, Galerkin projection, and variational structureFinite Element Methods · Calculation

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For

-u''(x)+u(x)=\sin(\pi

x) on 0<x<1, subject to u(0)=u(1)=0, use the trial function…

Solve approximately the variable-coefficient problem

-\frac{d}{dx}\!\left((1+x)u'(x)\right)=x

for 0<x<1, with…

Consider

-u''(x)=x^2

for 0<x<1, with u(0)=u(1)=0.

For -u''(x)+u(x)=1 on 0<x<1, with u(0)=u(1)=0, use

u_h(x)=a\,x(1-x)+b\,x^2(1-x)

.

Consider -u''(x)+u(x)=x on 0<x<1, with u(0)=u(1)=0, and restrict the approximation to

u_h(x)=a\,x(1-x)

.

Consider the boundary-value problem

-\big((1+x)u'(x)\big)'=2

on 0<x<1, with u(0)=0 and (1+x)u'(1)=5.

A bar on

0\le

x\le3

has piecewise-constant axial rigidity EA=2 for 0<x<1 and EA=5 for 1<x<3.

A single two-node linear bar element occupies

2\le

x\le5

, has cross-sectional area A=3, and has a spatially…

A stepped bar is represented by three nodes at

x_1=0

,

x_2=2

, and

x_3=3

.

Let a uniform bar on

0\le

x\le1

have EA=1, distributed load f(x)=1+x, prescribed displacement u(0)=0, and a…

The weak problem for a bar is: find

u\in H^1(0,2)

with

u(0)=1

such that…

A bar occupies

0\le

x\le2

, has constant EA=2, and is fixed at both ends: u(0)=u(2)=0.