INTRODUCTION
Jennifer L. Knihal appeals from an order of the district court for Douglas County granting Carolyn Gatzemeyer and Robert Gatzemeyer grandparent visitation with Knihal's two children. Based on the reasons that follow, we affirm.
BACKGROUND
On July 22, 2016, the Gatzemeyers filed a complaint for grandparent visitation seeking court-ordered visitation rights with their grandchildren, Michael Gatzemeyer and Maya Gatzemeyer. Knihal filed an answer opposing the complaint. During the pendency of the proceedings, the trial court awarded the Gatzemeyers temporary visitation with Michael and Maya, which visitation consisted of one overnight visit every other weekend.
The children's parents are Knihal and Kevin Gatzemeyer, the Gatzemeyers' son, who is now deceased. Knihal and Kevin were married in November 2004. Michael was born in 2004, and Maya was born in 2006. Knihal and Kevin separated in November 2008 and divorced in July 2010. Based on the parenting plan, Knihal and Kevin had joint physical custody *899of the children on a "week-on, week-off basis." Kevin died in March 2014.
The Gatzemeyers' complaint for visitation came on for trial on April 12, 2017. Carolyn testified that starting from the time of each child's birth until 2010, when Knihal and Kevin divorced, she and Robert would see the children at least weekly, if not more. Carolyn would babysit the children whenever Knihal and Kevin needed her to, usually once or twice per month, and sometimes the children would stay *633overnight. Carolyn testified that the children stayed with the Gatzemeyers on one or two occasions when Knihal and Kevin went out of town. She would also see the children during holidays and family events.
Carolyn testified that after Knihal and Kevin divorced in 2010 until the time of Kevin's death in 2014, she and Robert would see the children at least twice during the weeks Kevin had custody. Michael and Maya would stay overnight about every other week. Carolyn also testified that she took the children to daycare during Kevin's weeks of custody and would sometimes pick them up. She stated that she and Robert were very active in the children's lives.
The Gatzemeyers also hosted family dinners every other Sunday that were attended by Kevin, Michael, Maya, and Kevin's brother and his family. Carolyn testified that Michael and Maya also attended an annual summer family trip to Minnesota with Kevin, which included the Gatzemeyers and other extended family members.
Carolyn testified about the specific activities that she and Robert would do with the children. She and Robert would take the children to various places, including trips to a museum, a botanical garden, and a zoo. They would also watch movies and play cards together, which Carolyn said the children loved to do. Carolyn also testified that Michael loved hockey and that Kevin's brother was a hockey coach whose sons played hockey. The Gatzemeyers would take Michael to watch hockey games being coached by Kevin's brother and/or games that *900their cousins were playing. She testified about one occasion when Robert and Michael went to a hockey game together and she and Maya spent that time sewing at home.
Carolyn testified that one weekend she and Robert took the children to a state park, where they went swimming and hiking. Carolyn also testified that during the Minnesota trips, Michael and Maya loved swimming, boating, and playing outside. Carolyn further testified that she and Robert would attend the children's extracurricular activities, such as Michael's "ball games" and football games, as often as they could.
Carolyn testified that after Kevin died in March 2014, she and Robert continued to have regular contact with the children until March 2016. They would see the children "at least a couple times" per month, and the children would stay overnight with them once or twice per month. The time spent with the children was usually a result of Knihal's needing someone to watch the children. Sometimes, the children would call and ask if they could come over. Knihal allowed Michael and Maya to continue going to the Sunday dinners after Kevin passed away, and they also went on the family trip to Minnesota with the Gatzemeyers in 2014 and 2015.
Carolyn testified that on March 9, 2016, Knihal called her and said the Gatzemeyers "were horrible grandparents," and that she did not want them to have any future contact with the children. Carolyn testified that prior to March 9, her contact with Michael and Maya had been "regular and consistent since they were born" and that the children always enjoyed spending time with the Gatzemeyers.
Robert testified and concurred with Carolyn that they have had regular contact with the children since they were born. He also testified that he was involved in all the events and activities with Michael and Maya that Carolyn testified about.
The Gatzemeyers' daughter-in-law, who was married to Kevin's brother, testified that she has had the opportunity to observe the Gatzemeyers around Michael and Maya on numerous occasions. She testified *634that Carolyn loves to interact *901with the children, play with them, and take them places. She testified that Carolyn is "all about being a grandma" and that Robert "is a great grandpa." She also testified that the grandsons, including Michael, like to help Robert build and paint items in his woodshop and that Maya "adores" Robert. She testified that the contact between the Gatzemeyers and the children has been regular and consistent and that the relationship is a loving one.
Gabriel Butler, Knihal's boyfriend of 8 years and with whom she has lived for 6 years, also testified. He testified that before March 2016, the Gatzemeyers saw the children about once per month, sometimes for the day and sometimes overnight. He testified that after Kevin died, Michael and Maya would behave differently for a couple days after they came home from a visit with the Gatzemeyers. He testified they would yell and scream, would not listen to him or Knihal, and seemed to be upset with Knihal, even saying that she "killed" Kevin. Butler testified that the children's behavior after visits interfered with Knihal's ability to parent the children. He testified that since the temporary order has been in place, he had observed the same type of behavior when the children came home after visits. Butler testified that the visits under the temporary order have put a strain on Knihal's relationship with her children.
Butler acknowledged that Knihal had allowed regular contact between the Gatzemeyers and the children from the time of Kevin's death in March 2014 until March 2016, despite the children's behavior following the visits. He testified that the children love their grandparents and enjoy spending time with them. Butler testified that despite the behavior of the children after visits, he believed the children should still have contact with the Gatzemeyers and they should be involved in each other's lives.
Knihal testified that before she and Kevin separated in 2008, the children had regular contact with the Gatzemeyers. She said she did not know how much contact the children had *902after she and Kevin separated until he died. Knihal agreed with Carolyn's testimony that after Kevin died, the children would spend time with the Gatzemeyers about once a month and would sometimes stay overnight.
Knihal testified that prior to March 2016, when she told the Gatzemeyers they could no longer see the children, the children would behave differently when they came home from visits. She stated they would be defiant, disrespectful, and would make hurtful statements, such as saying it was her fault that Kevin is dead. Knihal testified that she believed the Gatzemeyers disparaged her when the children were visiting them. She testified that in March 2016, she "had had enough." Knihal testified that she called Carolyn and told her the children are upset and angry at Knihal when they return from visits and that Carolyn responded that what Knihal was saying was "not true and that [she was] over-exaggerating." Knihal told Carolyn that she did not want the Gatzemeyers to see the children again "until [she] was ready."
Knihal testified that since the temporary order has been in effect, the children have been exhibiting the same type of behavior after visits that they did before she ended visits in March 2016. She believed the time the children were spending with the Gatzemeyers was interfering with her parenting because the children would be mean and hurtful toward her and would not listen to her after visits. She also testified that in the month or two before trial, Maya has not wanted to attend the court-ordered visits.
*635Knihal testified that she believes it is in Michael's and Maya's best interests to have contact with the Gatzemeyers, but that she should be the one deciding when it should occur. She is opposed to court-ordered visitation because "it undermines [her] decision as their mother on whether or not they can see people when they want to."
Carolyn testified that neither she nor Robert have ever said anything negative about Knihal in front of the children and have never indicated that she was somehow responsible for *903Kevin's death. She further testified that she has never told anyone that she blames Knihal for Kevin's death.
Carolyn also denied that Knihal had ever told her that the children had behavior issues at home after visits. She stated that she had never heard that the children were acting out at home until it was mentioned in this lawsuit. Robert also testified that Knihal never told him that she was having trouble with the children after visits.
Following trial, the court entered an order finding that the Gatzemeyers had a significant beneficial relationship with the children, that it was in the best interests of the children that the Gatzemeyers be granted visitation, and that the Gatzemeyers' exercising visitation with the children would not adversely impact the parent-child relationship between the children and Knihal. The court granted the Gatzemeyers visitation with the children during the second weekend of each month from Saturday at 10 a.m. until Sunday at 7 p.m. The court also ordered visitation on Christmas Eve, the weekend before Easter, and each summer for the annual family trip to Minnesota.
ASSIGNMENTS OF ERROR
Knihal has assigned four errors, which we consolidate for discussion into two. Knihal assigns that the trial court erred in (1) granting the Gatzemeyers' request for grandparent visitation and (2) failing to give special weight to her determination of her children's best interests.
STANDARD OF REVIEW
Determinations concerning grandparent visitation are initially entrusted to the discretion of the trial judge, whose determinations, on appeal, will be reviewed de novo on the record and affirmed in the absence of an abuse of the trial judge's discretion. Vrtatko v. Gibson, 19 Neb. App. 83, 800 N.W.2d 676 (2011). A judicial abuse of discretion exists when a judge, within the effective limits of authorized judicial power, *904elects to act or refrain from action, but the selected option results in a decision which is untenable and unfairly deprives a litigant of a substantial right or a just result in matters submitted for disposition through a judicial system. Id.
ANALYSIS
Knihal first assigns that the trial court erred in granting the Gatzemeyers' request for grandparent visitation. The grandparent visitation statutes, Neb. Rev. Stat. §§ 43-1801 to 43-1803 (Reissue 2016), permit a grandparent to seek visitation with his or her minor grandchild in limited circumstances, including, as pertinent here, when the child's parent or parents are deceased. See § 43-1802(1)(a). A court can order grandparent visitation only if the petitioning grandparent proves by clear and convincing evidence that (1) there is, or has been, a significant beneficial relationship between the grandparent and the child; (2) it is in the best interests of the child that such relationship continue; and (3) such visitation will not adversely interfere with the parent-child relationship.
*636See, § 43-1802(2); Hamit v. Hamit, 271 Neb. 659, 715 N.W.2d 512 (2006). Clear and convincing evidence means that amount of evidence which produces in the trier of fact a firm belief or conviction about the existence of a fact to be proved. Nelson v. Nelson, 267 Neb. 362, 674 N.W.2d 473 (2004).
Knihal argues that the Gatzemeyers did not prove the three elements required under § 43-1802(2) by clear and convincing evidence. She first contends that there was not sufficient evidence that there is, or has been, a significant beneficial relationship between the Gatzemeyers and the children. The evidence showed that the Gatzemeyers have had a regular and consistent relationship with Michael and Maya from the time they were born, in 2004 and 2006 respectively, until March 2016, when Knihal stopped allowing the children to spend time with them. During Knihal and Kevin's marriage, the Gatzemeyers spent time with the children on a regular *905basis, sometimes having them overnight. After the divorce, the Gatzemeyers continued to see the children during the weeks Kevin had custody and helped Kevin get the children to and from daycare. The children would stay overnight sometimes as well. After Kevin died in March 2014, the Gatzemeyers continued to have regular contact with the children for the next 2 years. The children also continued to attend Sunday family dinners and went on the family trip to Minnesota in 2014 and 2015, as they had when Kevin was alive.
In addition to the amount of time the Gatzemeyers spent with the children, there was also evidence in regard to how the time was spent together and the quality of the relationship. The Gatzemeyers would take the children various places, such as the museum, the zoo, or hockey games, or they would spend time together at home watching movies or playing card games. Carolyn also testified that she and Robert would attend the children's extracurricular activities when they could.
The children's aunt testified that Carolyn loves to interact with the children, play with them, and take them places. The children's aunt further testified that the Gatzemeyers are good grandparents and have a loving relationship with the children. Butler testified that the children love their grandparents and enjoy spending time with them.
We conclude that the trial court did not abuse its discretion in finding that the Gatzemeyers presented clear and convincing evidence of a significant beneficial relationship with Michael and Maya.
Knihal also argues that the Gatzemeyers did not prove by clear and convincing evidence that it was in the children's best interests that the relationship continue, nor did they prove that visitation would not adversely interfere with Knihal's relationship with her children. Knihal contends that these two elements were not met based on the evidence of the children's behavior after visits with the Gatzemeyers.
Knihal testified that she ended Michael's and Maya's contact with the Gatzemeyers in March 2016 because of the *906children's defiant and disrespectful behavior after visits. She believed the Gatzemeyers disparaged her when the children were visiting. Knihal testified that she told Carolyn about the children's behavior in March 2016, but that Carolyn did not believe her. She further testified that since the temporary visitation order has been in place, the children are behaving the same way that they had in the past after visits. Butler agreed that the children behave differently after visits with the Gatzemeyers. Both Knihal and Butler testified that they believed *637that the visits were interfering with Knihal's ability to parent her children.
Despite Knihal's contention that the children had behavior issues when they returned from visits with the Gatzemeyers after Kevin's death, she allowed the children to continue to spend time with the Gatzemeyers for 2 years. She also testified that she believed it was in Michael's and Maya's best interests to continue to have contact with the Gatzemeyers. Butler also testified that he believed the children should have contact with the Gatzemeyers and they should be involved in each other's lives.
Carolyn testified that neither she nor Robert have ever said anything negative about Knihal in front of the children and have never indicated to them or anyone else that Knihal was somehow responsible for Kevin's death. Carolyn also denied that Knihal had ever told her that the children had behavior issues at home after visiting the Gatzemeyers, and Carolyn said that she heard the allegations for the first time during the present litigation. Robert also testified that Knihal never told him that the children were behaving differently after visits.
An appellate court will consider the fact that the trial court saw and heard the witnesses and observed their demeanor while testifying, and will give great weight to the trial court's judgment as to credibility. Hamit v. Hamit, 271 Neb. 659, 715 N.W.2d 512 (2006). After hearing the witnesses, the court apparently did not find Knihal's or Butler's testimony credible *907in regard to the children's behavior following visits. We defer to the trial court's findings on credibility.
As previously discussed, the Gatzemeyers have always been involved in the children's lives and they have spent time together, with and without other family members, on a regular, consistent basis. The evidence shows that the Gatzemeyers and the children have an established, loving relationship that is beneficial to the children. The relationship also allows Michael and Maya to stay connected with other paternal family members, which may not happen without visits with the Gatzemeyers. As previously stated, Knihal believed it was in Michael's and Maya's best interests to continue to have contact with the Gatzemeyers, she just did not want it to be court-ordered visitation.
We conclude that the trial court did not abuse its discretion in finding there was clear and convincing evidence that it was in the children's best interests that the relationship with the Gatzemeyers continue and that visitation between the children and the Gatzemeyers would not adversely interfere with the parent-child relationship.
Knihal also assigns that the trial court erred in failing to give special weight to her determination that visitation was not in her children's best interests. Knihal relies on principles established in Troxel v. Granville, 530 U.S. 57, 120 S.Ct. 2054, 147 L.Ed. 2d 49 (2000), which provide that a fit parent is presumed to act in the best interests of his or her child, and although special weight is to be accorded a fit parent's decision regarding visitation, the presumption in favor of a parent's decision is rebuttable. In Hamit v. Hamit, supra , the Nebraska Supreme Court determined that the requirements in § 43-1802(2) satisfy the principles established in Troxel v. Granville, supra . The Nebraska Supreme Court held that although the Nebraska grandparent visitation statutes recognize the interests of the child in the continuation of the grandparent relationship, under Nebraska's grandparent visitation statutes as a whole, the best interests of the child consideration *908does not deprive the parent *638of sufficient protection because visitation will not be awarded where such visitation would adversely interfere with the parent-child relationship. Hamit v. Hamit, supra .
In the present case, the court specifically found that visitation between the Gatzemeyers and the children would not adversely impact the parent-child relationship between Knihal and the children. The court gave Knihal's decision regarding visitation the weight it was entitled to based on § 43-1802(2) and Hamit v. Hamit, supra . Knihal's final assignment of error is without merit.
CONCLUSION
We conclude that the trial court did not err in granting grandparent visitation to the Gatzemeyers. Accordingly, the court's order is affirmed.
AFFIRMED .